A348895 Largest n-digit number such that the remainder after dividing by sum of digits is A348730(n).

9, 79, 799, 9887, 98999, 999599, 9999968, 99998989, 999989999, 9999989998, 99999999799, 999999999959, 9999999799999, 99999999998999, 999999999999797, 9999999999989999, 99999999999999988, 999999999999979999, 9999999999999998999, 99999899999999999989, 999999999999999899998

Offset

1,1

Comments

Subsequence of A348799.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..494

Prog

(Python)
from functools import lru_cache
from sympy.combinatorics.partitions import IntegerPartition
from sympy.utilities.iterables import partitions, multiset_permutations
@lru_cache(maxsize=None)
def intpartition(n, m): return tuple(''.join(str(d) for d in IntegerPartition(p).partition+[0]*(m-s)) for s, p in partitions(n, k=9, m=m, size=True))
def A348895(n):
    l, c, nmax, k = 9*n, 0, 0, 10**(n-1)
    while l > c:
        for p in intpartition(l, n):
            for q in multiset_permutations(p):
                w = int(''.join(q))
                if w >= k:
                    wr = w % l
                    if wr > c:
                        c = wr
                        nmax = w
                    if wr == c and nmax < w:
                        nmax = w
        l -= 1
    return nmax

Crossrefs

Cf. A348730, A348799, A348894.

Sequence in context: A083411 A181279 A173808 * A293723 A255807 A293916

Adjacent sequences: A348892 A348893 A348894 * A348896 A348897 A348898

Keyword

nonn,base

Author

Chai Wah Wu, Nov 02 2021

Status

approved