A052491 Smallest "inconsummate number" in base n: smallest number such that in base n, no number is this multiple of the sum of its digits.

13, 17, 29, 16, 27, 30, 42, 46, 62, 68, 86, 92, 114, 122, 147, 154, 182, 192, 222, 232, 266, 278, 314, 326, 367, 380, 422, 436, 482, 498, 546, 562, 614, 632, 688, 704, 762, 782, 842, 862, 926, 948, 1014, 1036, 1107, 1130, 1202, 1226, 1302, 1328, 1406, 1432

Offset

2,1

Links

Chai Wah Wu, Table of n, a(n) for n = 2..174

Example

a(10) = 62, from A003635.

Mathematica

Do[n = 1; While[k = n; While[ Apply[ Plus, IntegerDigits[k, b] ]*n != k && k < 100n, k += n ]; k != 100n, n++ ]; Print[n], {b, 2, 54} ]

Prog

(Python)
from itertools import count, combinations_with_replacement
from sympy.ntheory import digits
def A052491(n):
    for k in count(1):
        for l in count(1):
            if (n-1)*l*k < n**(l-1):
                return k
            for d in combinations_with_replacement(range(n), l):
                if (s:=sum(d)) > 0 and sorted(digits(s*k, n)[1:]) == list(d):
                    break
            else:
                continue
            break # Chai Wah Wu, May 09 2023

Crossrefs

Cf. A003635, A058898-A058907.

Sequence in context: A155923 A248215 A283135 * A283294 A283217 A283390

Adjacent sequences: A052488 A052489 A052490 * A052492 A052493 A052494

Keyword

nonn,nice,easy,base

Author

J. H. Conway, Dec 30 2000

Extensions

Corrected and extended by David Radcliffe, Jan 08 2001

More terms from David W. Wilson, Jan 10 2001

Status

approved