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

1,2

Comments

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

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

Links

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

Example

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.

Prog

(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)

Crossrefs

Sequence in context: A117350 A004239 A357670 * A260573 A224672 A039542

Adjacent sequences: A185814 A185815 A185816 * A185818 A185819 A185820

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Feb 07 2011

Status

approved