This kata is based on a [variation](https://www.codewars.com/kata/happy-numbers-5) of *Happy Numbers* by TySlothrop. It is advisable to complete it first to grasp the idea and then move on to this one.

___

Hello, my dear friend, and welcome to another *Happy Numbers* kata! What? You're not interested in them anymore? They are all the same? But what if I say that this one is a *performance version*...  

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# Your task:

Write a function `performant_numbers` which takes a number `n` as an argument and returns a list of all *happy numbers* from `1` to `n` inclusive. For example:

```
performant_numbers(10)   =>  [1, 7, 10]
performant_numbers(50)   =>  [1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49]
performant_numbers(100)  =>  [1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100]
```

# Test suite:

* `5000` tests with number `n` being up to `300000`
* The reference solution takes around `4.9` seconds to calculate the result
* you are not allowed to hardcode the sequence: you'll have to compute it (max length of the code: 1700 characters)

___

Will you take up the challenge?

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from bisect import bisect\n\nsieve = [None] * 300001\n\ndef is_happy(n):\n    seen = set()\n    while True:\n        if sieve[n] is not None:\n            return sieve[n], seen\n            \n        if n == 1:\n            break\n        elif n < 7:\n            return False, seen\n        seen.add(n)\n        n = sum(int(x)**2 for x in str(n))\n\n    return True, seen\n\n\nfor i in range(1, 300000+1):\n    state, seen = is_happy(i)\n    for x in seen:\n        sieve[x] = state\n\n\nFINAL = [1] + [idx for idx in range(1,300001) if sieve[idx]]\n\ndef performant_numbers(n):\n    first = 0\n    last = len(FINAL)-1\n    idx = float('inf')\n\n    while first <= last:\n        mid = (first+last)//2\n\n        if n == FINAL[mid]:\n            idx = mid+1\n            break\n        \n        elif n < FINAL[mid]:\n            idx = mid\n            last = mid - 1\n        \n        else:\n            first = mid + 1\n        \n    return FINAL[:idx]\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'performant_numbers'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5622