A390224 The smallest positive number k such that A066686(k,n) is a substring of A051129(n,k), or -1 if no such k exists.

-1, 250050005000, 11768, 32213, 2616, 5, 87, 25, 6, 32626422075, 866437799, 327239416, 8, 3650, 73698, 16, 87, 827210, 80522, 44, 30642, 279, 803014, 619, 49, 47, 1238, 234, 24, 29, 77, 736, 75, 109, 998, 175, 2259, 80, 3754, 13, 978, 73, 58157, 501, 38, 343, 73, 42

Offset

1,2

Links

Scott R. Shannon and Michael S. Branicky, Table of n, a(n) for n = 1..1000

Example

a(2) = 250050005000 as A066686(250050005000,2) = 2500500050002 is a substring of A051129(2,250050005000) = 250050005000^2 = 62525005000500025000000, and no number to the power of 2 smaller than 250050005000 satisfies this condition. See A018834.
a(6) = 5 as A066686(5,6) = 56 is a substring of A051129(6,5) = 5^6 = 15625, and no number to the power of 6 smaller than 5 satisfies this condition.

Prog

(Python)
from gmpy2 import digits, mpz
from itertools import count
def a(n):
    if n == 1: return -1
    strn = digits(n)
    return next(k for k in count(2) if digits(k)+strn in digits(mpz(k)**mpz(n)))

Crossrefs

Cf. A392669, A066686, A051129, A067599, A391639, A018834.

Sequence in context: A288477 A268846 A076254 * A213689 A348800 A015432

Adjacent sequences: A390221 A390222 A390223 * A390225 A390226 A390227

Keyword

sign,base

Author

Scott R. Shannon and Michael S. Branicky, Jan 19 2026

Status

approved