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

1,1

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A045537, A104782.

Sequence in context: A154349 A268068 A073601 * A228615 A267823 A063664

Adjacent sequences: A051245 A051246 A051247 * A051249 A051250 A051251

Keyword

nonn,base,nice

Author

Michel ten Voorde

Extensions

More terms from Jud McCranie

Status

approved