A121319 a(n) is the smallest number k such that k and 2^k have the same last n digits. Here k must have at least n digits (cf. A113627).

14, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 1075353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736

Offset

1,1

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..80

Jon E. Schoenfield, Excel program

Formula

If A109405(n) has n digits, a(n) = A109405(n), otherwise a(n) = A109405(n) + 10^n. - Max Alekseyev, May 05 2007

Example

2^14 = 16384 and 14 end with the same single digit 4, thus a(1) = 14.

Mathematica

f[n_] := Block[{k = If[n == 1, 2, 10], m = 10^n}, While[ PowerMod[2, k, m] != Mod[k, m], k += 2]; k]; Do[ Print@f@n, {n, 9}] (* Robert G. Wilson v *)

Prog

(PARI) A121319(n) = { local(k, tn); tn=10^n ; forstep(k=2, 1000000000, 2, if ( k % tn == (2^k) % tn, return(k) ; ) ; ) ; return(0) ; } { for(n = 1, 13, print( A121319(n)) ; ) ; } \\ R. J. Mathar, Aug 27 2006

Crossrefs

Cf. A007185, A016090, A003226, A035383, A064540, A064541, A109405.

Sequence in context: A279900 A263125 A113627 * A361994 A034181 A216766

Adjacent sequences: A121316 A121317 A121318 * A121320 A121321 A121322

Keyword

nonn,base

Author

Tanya Khovanova, Aug 25 2006

Extensions

a(6)-a(9) from Robert G. Wilson v and Jon E. Schoenfield, Aug 26 2006

a(10) from Robert G. Wilson v, Sep 26 2006

a(11)-a(16) from Alexander Adamchuk, Jan 28 2007

a(16) corrected by Max Alekseyev, Apr 12 2007

Status

approved