*This kata is inspired by [Project Euler Problem #387](https://projecteuler.net/problem=387)*

---

A [Harshad number](https://en.wikipedia.org/wiki/Harshad_number) (or Niven number) is a number that is divisible by the sum of its digits. A *right truncatable Harshad number* is any Harshad number that, when recursively right-truncated, results in a Harshad number at each truncation. By definition, 1-digit numbers are **not** right truncatable Harshad numbers.

For example `201` (which is a Harshad number) yields `20`, then `2` when right-truncated, which are all Harshad numbers. Thus `201` is a *right truncatable Harshad number*.


## Your task

Given a range of numbers (`(a, b)`, both included), return the list of right truncatable Harshad numbers in this range.

```if-not:javascript
Note: there are `500` random tests, with 0 <= `a` <= `b` <= 10^(16)
```
```if:javascript
Note: there are `500` random tests, with `0 <= a <= b <= Number.MAX_SAFE_INTEGER`
```

## Examples

```
0, 20        -->  [10, 12, 18, 20]
30, 100      -->  [30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100]
90, 200      -->  [90, 100, 102, 108, 120, 126, 180, 200]
200, 210     -->  [200, 201, 204, 207, 209, 210]
1000, 2000   -->  [1000, 1002, 1008, 1020, 1026, 1080, 1088, 1200, 1204, 1206, 1260, 1800, 2000]
2200, 2300   -->  []
9000002182976, 9000195371842  -->  [9000004000000, 9000004000008]
```

---

## My other katas

If you enjoyed this kata then please try [my other katas](https://www.codewars.com/collections/katas-created-by-anter69)! :-)

#### *Translations are welcome!*

Source: codewars | Difficulty: EASY
Tags: Mathematics

Starter code: def rthn_between(a, b):
	

Solutions:
def gen(n):
	if n >= 10 ** 16:
		return
	for i in range(10):
		x = 10 * n + i
		if x % sum(map(int, str(x))):
			continue
		yield x
		for y in gen(x):
			yield y
L = sorted((x for n in range(1, 10) for x in gen(n)))
from bisect import bisect_left as bl, bisect_right as br

def rthn_between(a, b):
	return L[bl(L, a):br(L, b)]


nums = list(range(1, 10))
(sums, rth) = (nums[:], [])
for _ in range(30):
	(nums_, sums_) = ([], [])
	for (n, s) in zip(nums, sums):
		for (n_, s_) in enumerate(range(s, s + 10), 10 * n):
			if not n_ % s_:
				nums_.append(n_)
				sums_.append(s_)
	(nums, sums) = (nums_, sums_)
	rth.extend(nums)
from bisect import bisect

def rthn_between(a, b):
	return rth[bisect(rth, a - 1):bisect(rth, b)]


is_harshad = lambda x: not x % sum(map(int, [*str(x)]))
li = [*list(range(1, 10))]
l = []
for i in range(15):
	li = [x * 10 + i for x in li for i in range(10) if is_harshad(x * 10 + i)]
	l.extend(li)
l.append(10 ** 16)

def rthn_between(a, b):
	return [x for x in l if a <= x <= b]


import itertools

def dig_sum(n):
	return sum([int(x) for x in str(n)])

def harshad_list(n):
	if n == 0:
		return []
	deci = [[1, 2, 3, 4, 5, 6, 7, 8, 9]]
	n -= 1
	while n != 0:
		temp = []
		for d in deci[-1]:
			e = 10 * d
			for tail in range(10):
				if (e + tail) % dig_sum(e + tail) == 0:
					temp.append(e + tail)
		n -= 1
		deci.append(temp)
	return deci
pre_calc = list(itertools.chain.from_iterable(harshad_list(16)))

def rthn_between(a, b):
	res = []
	for i in pre_calc:
		if i >= a and i <= b:
			if i > 9:
				res.append(i)
	return res


import functools
import itertools

def rthn_between(a, b):
	k1 = len(str(b)) + 1
	k0 = len(str(a)) - 1
	harshads = set.union(*map(n_part_harshad, range(k0, k1)))
	return sorted([i for i in harshads if i in range(max(10, a), b + 1)])

@functools.lru_cache(None)
def n_part_harshad(k):
	vals = set(range(10))
	if k < 1:
		return vals - {0}
	prevs = n_part_harshad(k - 1)
	groups = (10 * a + b for (a, b) in itertools.product(prevs, vals))
	return set(filter(part_harshad, groups))

def r_harshad(n):
	k = str(n)
	vals = (int(k[:i]) for i in range(1, len(k) + 1))
	return n > 9 and all(map(part_harshad, vals))

@functools.lru_cache(None)
def part_harshad(n):
	return n % dig_sum(n) == 0

def dig_sum(n):
	return sum(map(int, str(n)))


HARSHED = [10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 120, 126, 180, 200, 201, 204, 207, 209, 210, 216, 240, 243, 247, 270, 300, 306, 308, 360, 364, 400, 402, 405, 407, 408, 420, 423, 450, 480, 481, 486, 500, 504, 506, 540, 600, 603, 605, 630, 700, 702, 704, 720, 800, 801, 803, 804, 810, 840, 846, 900, 902, 1000, 1002, 1008, 1020, 1026, 1080, 1088, 1200, 1204, 1206, 1260, 1800, 2000, 2001, 2004, 2007, 2010, 2016, 2040, 2043, 2070, 2090, 2100, 2106, 2160, 2400, 2401, 2403, 2408, 2430, 2470, 2478, 2700, 2704, 3000, 3006, 3060, 3080, 3600, 3640, 4000, 4002, 4005, 4008, 4020, 4023, 4050, 4070, 4080, 4086, 4200, 4203, 4230, 4500, 4800, 4802, 4806, 4807, 4809, 4810, 4860, 5000, 5004, 5040, 5044, 5060, 5066, 5400, 6000, 6003, 6030, 6050, 6300, 7000, 7002, 7020, 7040, 7200, 7208, 8000, 8001, 8004, 8010, 8030, 8040, 8046, 8100, 8400, 8406, 8460, 8463, 9000, 9020, 9022, 10000, 10002, 10008, 10020, 10024, 10026, 10080, 10200, 10206, 10208, 10260, 10268, 10800, 10802, 10880, 12000, 12006, 12040, 12042, 12060, 12064, 12600, 18000, 20000, 20001, 20004, 20007, 20009, 20010, 20016, 20040, 20041, 20043, 20048, 20070, 20100, 20104, 20106, 20108, 20160, 20400, 20403, 20405, 20430, 20700, 20702, 20900, 21000, 21006, 21060, 21600, 24000, 24003, 24010, 24012, 24030, 24038, 24080, 24084, 24087, 24300, 24700, 24780, 24786, 27000, 27040, 27048, 30000, 30006, 30008, 30060, 30600, 30602, 30800, 36000, 36400, 40000, 40002, 40005, 40007, 40008, 40020, 40023, 40027, 40050, 40080, 40082, 40086, 40089, 40200, 40201, 40203, 40205, 40208, 40230, 40500, 40502, 40700, 40800, 40806, 40860, 42000, 42003, 42030, 42300, 45000, 48000, 48006, 48020, 48024, 48027, 48060, 48070, 48090, 48100, 48600, 50000, 50004, 50006, 50040, 50048, 50400, 50402, 50440, 50600, 50660, 54000, 60000, 60003, 60005, 60030, 60034, 60300, 60302, 60500, 60502, 63000, 70000, 70002, 70004, 70020, 70200, 70202, 70400, 72000, 72080, 80000, 80001, 80003, 80004, 80010, 80040, 80041, 80046, 80047, 80100, 80102, 80300, 80400, 80402, 80406, 80409, 80460, 81000, 84000, 84006, 84060, 84063, 84065, 84600, 84630, 90000, 90002, 90200, 90220, 100000, 100002, 100008, 100020, 100026, 100080, 100200, 100206, 100240, 100242, 100260, 100800, 102000, 102004, 102006, 102060, 102068, 102080, 102600, 102680, 108000, 108004, 108020, 108800, 120000, 120006, 120060, 120400, 120402, 120406, 120420, 120428, 120600, 120640, 126000, 180000, 200000, 200001, 200004, 200007, 200010, 200016, 200040, 200043, 200070, 200090, 200100, 200106, 200160, 200400, 200403, 200410, 200412, 200430, 200434, 200480, 200484, 200487, 200700, 201000, 201006, 201040, 201042, 201060, 201080, 201600, 201604, 204000, 204001, 204003, 204008, 204030, 204050, 204300, 207000, 207020, 207026, 209000, 210000, 210006, 210060, 210600, 216000, 240000, 240003, 240030, 240100, 240102, 240120, 240300, 240380, 240800, 240804, 240807, 240840, 240870, 243000, 247000, 247800, 247802, 247806, 247860, 270000, 270400, 270480, 270486, 300000, 300006, 300060, 300080, 300600, 306000, 306020, 308000, 308006, 360000, 364000, 364004, 400000, 400002, 400005, 400008, 400020, 400023, 400050, 400070, 400080, 400086, 400200, 400203, 400230, 400270, 400500, 400504, 400800, 400806, 400820, 400824, 400827, 400860, 400868, 400869, 400890, 400896, 402000, 402003, 402010, 402012, 402030, 402050, 402080, 402084, 402087, 402300, 405000, 405008, 405020, 407000, 408000, 408002, 408006, 408009, 408060, 408600, 420000, 420003, 420030, 420300, 420308, 423000, 450000, 480000, 480006, 480060, 480200, 480204, 480207, 480240, 480249, 480270, 480276, 480600, 480700, 480708, 480900, 481000, 486000, 486001, 486003, 500000, 500004, 500040, 500060, 500400, 500480, 504000, 504020, 504400, 506000, 506008, 506600, 506604, 540000, 600000, 600003, 600030, 600050, 600058, 600300, 600340, 600348, 603000, 603020, 605000, 605020, 630000, 700000, 700002, 700020, 700024, 700040, 700200, 702000, 702020, 704000, 704002, 720000, 720800, 720804, 800000, 800001, 800004, 800010, 800030, 800040, 800046, 800100, 800400, 800406, 800410, 800460, 800469, 800470, 801000, 801020, 803000, 804000, 804006, 804020, 804024, 804027, 804060, 804061, 804090, 804600, 810000, 810004, 840000, 840006, 840060, 840063, 840600, 840630, 840650, 840658, 846000, 846300, 900000, 900020, 902000, 902200, 1000000, 1000002, 1000006, 1000008, 1000020, 1000026, 1000080, 1000200, 1000206, 1000208, 1000260, 1000800, 1000802, 1002000, 1002006, 1002060, 1002400, 1002402, 1002420, 1002600, 1008000, 1020000, 1020006, 1020008, 1020040, 1020042, 1020060, 1020068, 1020600, 1020602, 1020604, 1020680, 1020684, 1020800, 1026000, 1026800, 1080000, 1080002, 1080040, 1080044, 1080200, 1088000, 1200000, 1200006, 1200060, 1200600, 1200608, 1204000, 1204002, 1204020, 1204060, 1204200, 1204280, 1206000, 1206400, 1206408, 1260000, 1800000, 2000000, 2000001, 2000004, 2000005, 2000007, 2000009, 2000010, 2000016, 2000040, 2000043, 2000070, 2000100, 2000106, 2000108, 2000160, 2000400, 2000403, 2000405, 2000430, 2000700, 2000702, 2000900, 2001000, 2001006, 2001060, 2001064, 2001600, 2004000, 2004003, 2004030, 2004100, 2004102, 2004106, 2004120, 2004300, 2004340, 2004800, 2004804, 2004807, 2004840, 2004870, 2007000, 2010000, 2010006, 2010008, 2010060, 2010400, 2010402, 2010404, 2010420, 2010424, 2010600, 2010602, 2010800, 2010808, 2016000, 2016040, 2040000, 2040003, 2040005, 2040010, 2040012, 2040030, 2040080, 2040084, 2040087, 2040300, 2040302, 2040500, 2043000, 2070000, 2070002, 2070200, 2070260, 2070264, 2090000, 2100000, 2100006, 2100060, 2100600, 2106000, 2160000, 2400000, 2400003, 2400030, 2400034, 2400300, 2401000, 2401002, 2401020, 2401200, 2401204, 2403000, 2403800, 2408000, 2408004, 2408007, 2408040, 2408041, 2408049, 2408070, 2408076, 2408400, 2408700, 2430000, 2470000, 2478000, 2478006, 2478020, 2478060, 2478600, 2700000, 2700008, 2704000, 2704800, 2704806, 2704860, 3000000, 3000004, 3000006, 3000008, 3000060, 3000600, 3000602, 3000800, 3000806, 3006000, 3006008, 3060000, 3060002, 3060200, 3080000, 3080060, 3600000, 3640000, 3640040, 4000000, 4000002, 4000003, 4000005, 4000007, 4000008, 4000009, 4000020, 4000023, 4000050, 4000080, 4000086, 4000200, 4000203, 4000205, 4000230, 4000500, 4000502, 4000508, 4000700, 4000800, 4000806, 4000860, 4002000, 4002003, 4002030, 4002038, 4002300, 4002700, 4005000, 4005040, 4008000, 4008005, 4008006, 4008060, 4008069, 4008200, 4008204, 4008207, 4008240, 4008270, 4008600, 4008601, 4008609, 4008680, 4008690, 4008900, 4008906, 4008960, 4020000, 4020003, 4020005, 4020030, 4020100, 4020102, 4020104, 4020120, 4020300, 4020302, 4020500, 4020800, 4020804, 4020807, 4020808, 4020840, 4020848, 4020870, 4023000, 4050000, 4050002, 4050080, 4050200, 4050202, 4070000, 4080000, 4080006, 4080020, 4080024, 4080027, 4080060, 4080090, 4080600, 4080604, 4086000, 4200000, 4200003, 4200030, 4200300, 4203000, 4203004, 4203080, 4230000, 4230008, 4500000, 4800000, 4800006, 4800060, 4800068, 4800600, 4802000, 4802004, 4802007, 4802009, 4802040, 4802041, 4802070, 4802400, 4802408, 4802409, 4802490, 4802700, 4802706, 4802760, 4806000, 4807000, 4807080, 4809000, 4810000, 4810008, 4860000, 4860010, 4860030, 5000000, 5000002, 5000004, 5000006, 5000008, 5000040, 5000400, 5000402, 5000600, 5004000, 5004800, 5004804, 5040000, 5040002, 5040200, 5044000, 5044006, 5060000, 5060080, 5066000, 5066040, 5400000, 6000000, 6000001, 6000003, 6000005, 6000007, 6000008, 6000030, 6000300, 6000302, 6000500, 6000580, 6000582, 6000588, 6003000, 6003400, 6003480, 6030000, 6030002, 6030200, 6030206, 6050000, 6050200, 6300000, 7000000, 7000002, 7000004, 7000006, 7000020, 7000200, 7000202, 7000240, 7000246, 7000400, 7002000, 7020000, 7020002, 7020200, 7040000, 7040006, 7040020, 7200000, 7208000, 7208040, 8000000, 8000001, 8000003, 8000004, 8000005, 8000006, 8000010, 8000040, 8000046, 8000100, 8000102, 8000300, 8000400, 8000406, 8000460, 8001000, 8004000, 8004006, 8004060, 8004069, 8004100, 8004108, 8004600, 8004609, 8004690, 8004700, 8010000, 8010002, 8010200, 8030000, 8030008, 8040000, 8040006, 8040060, 8040200, 8040204, 8040207, 8040208, 8040240, 8040249, 8040270, 8040276, 8040600, 8040604, 8040610, 8040900, 8046000, 8046003, 8100000, 8100040, 8400000, 8400006, 8400060, 8400063, 8400600, 8400630, 8406000, 8406008, 8406300, 8406500, 8406504, 8406580, 8460000, 8463000, 9000000, 9000002, 9000004, 9000200, 9020000, 9022000, 10000000, 10000002, 10000008, 10000020, 10000026, 10000060, 10000062, 10000080, 10000200, 10000206, 10000260, 10000800, 10002000, 10002006, 10002060, 10002080, 10002086, 10002600, 10008000, 10008020, 10020000, 10020006, 10020060, 10020600, 10024000, 10024002, 10024020, 10024200, 10026000, 10080000, 10200000, 10200006, 10200060, 10200068, 10200080, 10200400, 10200402, 10200420, 10200424, 10200600, 10200680, 10200682, 10206000, 10206020, 10206040, 10206800, 10206840, 10208000, 10260000, 10268000, 10800000, 10800020, 10800400, 10800440, 10802000, 10880000, 12000000, 12000006, 12000060, 12000600, 12006000, 12006080, 12040000, 12040002, 12040020, 12040200, 12040600, 12042000, 12042004, 12042800, 12060000, 12064000, 12064080, 12064086, 12600000, 18000000, 18000008, 20000000, 20000001, 20000004, 20000007, 20000010, 20000016, 20000040, 20000043, 20000050, 20000052, 20000070, 20000090, 20000100, 20000106, 20000160, 20000400, 20000403, 20000430, 20000700, 20001000, 20001006, 20001060, 20001080, 20001600, 20004000, 20004003, 20004030, 20004050, 20004300, 20004308, 20007000, 20007020, 20009000, 20009002, 20010000, 20010004, 20010006, 20010060, 20010600, 20010640, 20010648, 20016000, 20040000, 20040003, 20040007, 20040030, 20040300, 20041000, 20041002, 20041020, 20041028, 20041060, 20041200, 20043000, 20043400, 20043408, 20048000, 20048004, 20048007, 20048040, 20048070, 20048400, 20048401, 20048700, 20070000, 20100000, 20100006, 20100060, 20100080, 20100086, 20100600, 20104000, 20104002, 20104006, 20104020, 20104040, 20104200, 20104240, 20106000, 20106020, 20106028, 20108000, 20108080, 20108088, 20160000, 20160400, 20160406, 20400000, 20400003, 20400030, 20400050, 20400100, 20400102, 20400120, 20400300, 20400800, 20400804, 20400807, 20400840, 20400848, 20400849, 20400870, 20400876, 20403000, 20403020, 20403026, 20405000, 20430000, 20700000, 20700004, 20700020, 20702000, 20702600, 20702640, 20900000, 21000000, 21000006, 21000060, 21000600, 21006000, 21060000, 21060008, 21600000, 24000000, 24000003, 24000030, 24000300, 24000340, 24003000, 24010000, 24010002, 24010020, 24010200, 24012000, 24012040, 24030000, 24038000, 24038002, 24080000, 24080004, 24080007, 24080040, 24080070, 24080400, 24080409, 24080410, 24080490, 24080496, 24080700, 24080706, 24080760, 24084000, 24084001, 24084008, 24087000, 24300000, 24700000, 24780000, 24780006, 24780060, 24780200, 24780600, 24786000, 27000000, 27000080, 27040000, 27048000, 27048006, 27048060, 27048600, 30000000, 30000006, 30000040, 30000042, 30000060, 30000080, 30000088, 30000600, 30006000, 30006020, 30008000, 30008060, 30060000, 30060004, 30060080, 30600000, 30600020, 30602000, 30602006, 30602008, 30800000, 30800600, 36000000, 36400000, 36400400, 40000000, 40000002, 40000005, 40000008, 40000020, 40000023, 40000030, 40000032, 40000050, 40000070, 40000080, 40000086, 40000090, 40000200, 40000203, 40000207, 40000230, 40000500, 40000800, 40000806, 40000860, 40000863, 40002000, 40002003, 40002030, 40002050, 40002300, 40005000, 40005004, 40005020, 40005080, 40005084, 40007000, 40007008, 40008000, 40008006, 40008060, 40008600, 40020000, 40020001, 40020003, 40020008, 40020030, 40020300, 40020380, 40023000, 40027000, 40027008, 40050000, 40050400, 40080000, 40080001, 40080006, 40080050, 40080054, 40080060, 40080069, 40080600, 40080605, 40080609, 40080690, 40082000, 40082004, 40082007, 40082040, 40082070, 40082400, 40082700, 40086000, 40086009, 40086010, 40086090, 40086800, 40086900, 40089000, 40089006, 40089060, 40089600, 40200000, 40200003, 40200030, 40200050, 40200300, 40200308, 40201000, 40201002, 40201020, 40201040, 40201200, 40203000, 40203020, 40205000, 40208000, 40208004, 40208007, 40208040, 40208049, 40208070, 40208076, 40208080, 40208400, 40208480, 40208481, 40208487, 40208700, 40230000, 40500000, 40500020, 40500800, 40502000, 40502020, 40502024, 40502028, 40700000, 40700006, 40800000, 40800006, 40800060, 40800200, 40800204, 40800207, 40800240, 40800270, 40800600, 40800900, 40806000, 40806003, 40806040, 40806045, 40860000, 42000000, 42000003, 42000030, 42000300, 42003000, 42030000, 42030040, 42030800, 42300000, 42300080, 45000000, 48000000, 48000006, 48000060, 48000061, 48000600, 48000603, 48000680, 48000681, 48006000, 48020000, 48020004, 48020007, 48020040, 48020070, 48020090, 48020094, 48020400, 48020410, 48020418, 48020700, 48024000, 48024001, 48024009, 48024080, 48024090, 48024900, 48027000, 48027006, 48027060, 48027600, 48027606, 48060000, 48070000, 48070800, 48090000, 48100000, 48100004, 48100080, 48600000, 48600100, 48600104, 48600108, 48600300, 50000000, 50000004, 50000020, 50000022, 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9022000008008000]
rthn_between = lambda a, b: [i for i in HARSHED if a <= i <= b]


harshad = [1, 2, 3, 4, 5, 6, 7, 8, 9]
current = [1, 2, 3, 4, 5, 6, 7, 8, 9]
for i in range(2, 17):
	new = []
	for curr in current:
		for d in range(0, 10):
			if int(str(curr) + str(d)) % sum([int(f) for f in str(curr) + str(d)]) == 0:
				new.append(int(str(curr) + str(d)))
	harshad += new
	current = [d for d in new]
harshad = harshad[9:]
t = len(harshad)

def rthn_between(a, b):
	i1 = 0
	i2 = t
	c1 = -1
	c2 = -1
	f = 0
	while i2 - i1 > 1:
		f = (i1 + i2) // 2
		if harshad[f] < a:
			i1 = f
		else:
			i2 = f
	c1 = i2 if harshad[i1] < a else i1
	i1 = 0
	i2 = t
	while i2 - i1 > 1:
		f = (i1 + i2) // 2
		if harshad[f] < b:
			i1 = f
		else:
			i2 = f
	c2 = i2 if harshad[i1] < b else i1
	return [d for d in harshad[c1:c2 + 1] if a <= d <= b]