A185817 Smallest m such that n is a prefix of 101^m in its decimal representation.

0, 70, 111, 140, 162, 181, 196, 209, 221, 1, 10, 19, 27, 34, 41, 48, 54, 60, 65, 70, 75, 80, 84, 88, 93, 97, 100, 104, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 137, 140, 142, 145, 147, 149, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 175, 177, 179, 181

Offset: 1

Author

Reinhard Zumkeller, Feb 07 2011

Keywords

• nonn
• base
• look

Comments

a(n) = MIN{e: floor(A096884(e)/10^k) = n for some k}.

a(n) <= a(10*n + d), 0 <= d < 10.

Examples

			a(1) = 0; a(10) = 1; a(101) = 1;
a(2) = 70, as A000030(101^e) = 1 for e < 70 and A000030(101^70) = 2,
101^70=2006763368395383712973746195325904225117468781576180838692428661200863034768\
95435690179367146267108054577096030854694073677909106884264157001.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..7777

Crossrefs

Cf. A000030, A096884,

Programs

Haskell

import Data.List (isPrefixOf)
a185817 n = pref101pow 0 1 where
   pref101pow e pow101 = if isPrefixOf (show n) (show pow101)
                            then e
                            else pref101pow (e + 1) (101 * pow101)