We have the first value of a certain sequence, we will name it ```initVal```.
We define  pattern list, ```patternL```, an array that has the differences between contiguous terms of the sequence.
``` E.g: patternL = [k1, k2, k3, k4]``` 

The terms of the sequence will be such values that:
```python
term1 = initVal
term2 - term1 = k1
term3 - term2 = k2
term4 - term3 = k3
term5 - term4 = k4
term6 - term5 = k1
term7 - term6 = k2
term8 - term7 = k3
term9 - term8 = k4
....  - ..... = ...
....  - ..... = ...
 ``` 
So the values of the differences between contiguous terms are cyclical and are  repeated as the differences values of the pattern list stablishes.

Let's see an example with numbers:
```python
initVal = 10
patternL = [2, 1, 3]
term1 = 10
term2 = 12
term3 = 13
term4 = 16
term5 = 18
term6 = 19
term7 = 22  # and so on...
```
We can easily obtain the next terms of the sequence following the values in the pattern list.
We see that the sixth term of the sequence, ```19```, has the sum of its digits ```10```.

Make a function ```sumDig_nthTerm()```, that receives three arguments in this order 

 ```sumDig_nthTerm(initVal, patternL, nthTerm(ordinal number of the term in the sequence)) ```

This function will output the sum of the digits of the n-th term of the sequence.

Let's see some cases for this function:
```python
sumDig_nthTerm(10, [2, 1, 3], 6) -----> 10 # because the sixth term is 19 sum of Dig = 1 + 9 = 10. The sequence up to the sixth-Term is: 10, 12, 13, 16, 18, 19

sumDig_nthTerm(10, [1, 2, 3], 15) ----> 10 # 37 is the 15-th term, and 3 + 7 = 10
```
Enjoy it and happy coding!!

```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 = 'def sumDig_nthTerm(base, cycle, k):\n    loop, remaining = divmod(k - 1, len(cycle))\n    term = base + loop * sum(cycle) + sum(cycle[:remaining])\n    return sum(int(d) for d in str(term))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'sumDig_nthTerm'
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: 5749