A061280 Smallest base b >= 2 for which b^n contains n as a substring.

10, 5, 7, 7, 5, 2, 3, 7, 3, 2, 11, 7, 6, 25, 7, 11, 4, 8, 5, 7, 6, 6, 6, 3, 4, 9, 17, 3, 6, 13, 8, 5, 8, 5, 2, 2, 2, 8, 6, 6, 5, 4, 7, 2, 6, 9, 8, 6, 2, 4, 2, 8, 6, 5, 5, 5, 3, 8, 4, 2, 3, 3, 6, 5, 6, 12, 2, 6, 3, 5, 3, 2, 2, 6, 5, 6, 3, 3, 4, 3, 4, 2, 3, 4, 2, 4, 3, 7, 2, 8, 8, 4, 2, 6, 3, 4, 7, 6, 7, 7

Offset: 1

Author

Erich Friedman, Jun 06 2001

Keywords

• base
• easy
• look
• nonn

Examples

			a(3) = 7 since 7^1 contains no 1, 7^2 contains no 2 and 7^3 contains a 3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Programs

Maple

a:= proc(n) local b; for b from 2 while
      searchtext(""||n, ""||(b^n))=0 do od; b
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 28 2016

Mathematica

Table[b = 2; While[Length@ SequencePosition[IntegerDigits[b^n], IntegerDigits[n]] == 0, b++]; b, {n, 120}] (* Michael De Vlieger, Sep 28 2016, Version 10.1 *)

Python

def a(n):
    b, s = 2, str(n)
    while s not in str(b**n): b += 1
    return b
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Oct 05 2021