A051248 n^a(n) is the smallest power of n (with a(n) > 1) which starts with n.

2, 8, 18, 6, 24, 10, 20, 11, 22, 2, 26, 14, 10, 8, 92, 6, 166, 5, 19, 11, 60, 39, 48, 51, 94, 42, 467, 86, 14, 66, 58, 3, 5268, 33, 58, 10, 45, 70, 23, 6, 205, 70, 31, 15, 50, 84, 248, 70, 72, 94, 107, 170, 30, 10139, 182, 136, 87, 318, 49, 10, 178, 237, 295, 99, 17, 206

Offset: 1

Author

Michel ten Voorde

Keywords

• nonn
• base
• nice

Comments

A070327(n) = n^a(n) for n > 1. - Reinhard Zumkeller, Sep 29 2011

The largest of the first 10000 terms is a(1955) = 119589011. - Giovanni Resta, May 27 2016

Examples

			2^8 = 256 begins with 2, and 2^k does not begin with 2 for any smaller integer k > 1, so a(2) = 8.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 275 terms from Reinhard Zumkeller)

Crossrefs

Cf. A045537, A104782.

Programs

Haskell

import Data.List (isPrefixOf)
a051248 n = 2 + length
   (takeWhile (not . (show n `isPrefixOf`) . show) $ iterate (* n) (n^2))
-- Reinhard Zumkeller, Sep 29 2011

Mathematica

f[n_]:=Module[{i=2},While[Take[IntegerDigits[n^i],IntegerLength[n]] != IntegerDigits[n],i++];i]; Array[f,70] (* Harvey P. Dale, Oct 04 2011 *)

Python

from itertools import count
def a(n):
    s = str(n)
    return next(e for e in count(2) if str(n**e).startswith(s))
print([a(n) for n in range(1, 33)]) # Michael S. Branicky, Feb 23 2025

Extensions

More terms from Jud McCranie