A348894 Smallest n-digit number such that the remainder after dividing by sum of digits is A348730(n).

1, 79, 799, 9599, 98999, 599999, 8999998, 89998999, 899999999, 9899999998, 99988999999, 779999999999, 8999899999999, 89999999999999, 799899999999998, 9999989999999999, 89999999989999999, 799999999999999999, 9999999999999998999, 88999999999999999999, 899999999899999999999

Offset

1,2

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 A348894(n):
    l, c, nmin, k = 9*n, 0, 10**n-1, 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
                        nmin = w
                    if wr == c and nmin > w:
                        nmin = w
        l -= 1
    return nmin

Crossrefs

Cf. A348730, A348799.

Sequence in context: A251373 A251366 A152034 * A142816 A093279 A194785

Adjacent sequences: A348891 A348892 A348893 * A348895 A348896 A348897

Keyword

nonn,base

Author

Chai Wah Wu, Nov 02 2021

Status

approved