A061381 Smallest "inconsummate number" in base n greater than in the previous base.

13, 17, 29, 46, 64, 86, 105, 136, 161, 200, 229, 276, 309, 362, 419, 460, 505, 572, 621, 694, 749, 830, 889, 978, 1054, 1136, 1205, 1306, 1381, 1490, 1569, 1684, 1769, 1892, 1999, 2112, 2205, 2342, 2441, 2584, 2689, 2840, 2949, 3106, 3269, 3386, 3505, 3678

Offset: 2

Author

Robert G. Wilson v, Jun 08 2001

Keywords

• base
• easy
• nice
• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..226

Crossrefs

Cf. A052491.

Programs

Mathematica

n = 1; Do[ While[k = n; While[ Apply[ Plus, IntegerDigits[k, b] ]*n != k && k < 100n, k += n]; k != 100n, n++ ]; Print[n], {b, 2, 60} ]

Python

from functools import lru_cache
from itertools import count, combinations_with_replacement
from sympy.ntheory import digits
@lru_cache(maxsize=None)
def A061381(n):
    for k in count((0 if n <= 2 else A061381(n-1))+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