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

Author

J. H. Conway, Dec 30 2000

Keywords

• nonn
• nice
• easy
• base

Examples

			a(10) = 62, from A003635.
		

Links

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

Crossrefs

Cf. A003635, A058898-A058907.

Programs

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} ]

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

Extensions

Corrected and extended by David Radcliffe, Jan 08 2001

More terms from David W. Wilson, Jan 10 2001