OFFSET
1,1
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
In general, no prime p is a term since they are a power of base p.
Numbers having a single digit are not terms:
1 is not a term since 1 is a power of all bases b;
Composites 4, 6, and 9 are not in the sequence since 4 = 2^2, 6 = 2*3, and 9 = 3^2.
10 is not a term since it ends in a single zero, and zero is not a power of another number.
a(1) = 12 since it is not a perfect power, 2 | 12, and 12 mod 10 is a power of 2.
a(2) = 14 since it is not a perfect power, 2 | 14, and 14 mod 10 is a power of 2.
20 is not a term since it ends with a zero, and zero is not a power of another number.
26 is not a term since 6 does not divide 26.
1100 is a term since it is not a perfect power, 100 = 100^1, and 100 | 1100.
MATHEMATICA
nn = 130; t = Union@ Flatten@ Table[m = 10^IntegerLength[b] + b; If[m > nn, Nothing, s = b^Range[0, Floor@ Log[b, nn]]; Flatten@ Reap[Map[(w = IntegerDigits[#]; i = 0; While[Set[k, FromDigits@ Join[IntegerDigits[i], w]] <= nn, If[And[Divisible[k, b], FreeQ[s, k]], Sow[k]]; i++]) &, s] ][[-1]]], {b, 2, nn}]; Select[t, GCD @@ FactorInteger[#][[;; , -1]] === 1 &]
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Stefano Spezia and Michael De Vlieger, Jun 28 2025
STATUS
approved