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A185817 Smallest m such that n is a prefix of 101^m in its decimal representation. 2

%I #16 Jan 29 2014 04:03:32

%S 0,70,111,140,162,181,196,209,221,1,10,19,27,34,41,48,54,60,65,70,75,

%T 80,84,88,93,97,100,104,108,111,114,117,120,123,126,129,132,135,137,

%U 140,142,145,147,149,152,154,156,158,160,162,164,166,168,170,172,174,175,177,179,181

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

%C a(n) = MIN{e: floor(A096884(e)/10^k) = n for some k;

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

%H Reinhard Zumkeller, <a href="/A185817/b185817.txt">Table of n, a(n) for n = 1..7777</a>

%e a(1) = 0; a(10) = 1; a(101) = 1;

%e a(2) = 70, as A000030(101^e) = 1 for e < 70 and A000030(101^70) = 2,

%e 101^70=2006763368395383712973746195325904225117468781576180838692428661200863034768\

%e 95435690179367146267108054577096030854694073677909106884264157001.

%o (Haskell)

%o import Data.List (isPrefixOf)

%o a185817 n = pref101pow 0 1 where

%o pref101pow e pow101 = if isPrefixOf (show n) (show pow101)

%o then e

%o else pref101pow (e + 1) (101 * pow101)

%K nonn,base,look

%O 1,2

%A _Reinhard Zumkeller_, Feb 07 2011

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