A181610 The last n digits of powers of 2 start cycling. a(n) is the number of zero-free terms in this cycle.

4, 18, 81, 364, 1638, 7371, 33170, 149268, 671701, 3022653, 13601945, 61208743, 275439346, 1239477074, 5577646830, 25099410745, 112947348510, 508263067945, 2287183805359, 10292327123878, 46315472056678, 208419624257654, 937888309161430, 4220497391215744

Offset

1,1

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..26

Example

The last two digits of powers of two cycle through 20 terms (A000855): 04, 08, 16, 32, 64, 28, 56, 12, 24, 48, 96, 92, 84, 68, 36, 72, 44, 88, 76, 52. Out of those 18 do not contain a zero. Hence a(2) = 18.

Mathematica

f[n_] := Block[{c = 0, k = n, lmt = n + 4*5^(n - 1)},
While[k < lmt, m = PowerMod[2, k, 10^n];
  If[m >= 10^(n - 1) && !MemberQ[ IntegerDigits@ m, 0], c++ ]; k++ ]; c];
Array[ f, 11] (* Robert G. Wilson v, Jan 30 2011 *)

Crossrefs

The corresponding cycle length is A005054. See A126605 for n=3.

Sequence in context: A252823 A264191 A257060 * A264927 A257059 A194460

Adjacent sequences: A181607 A181608 A181609 * A181611 A181612 A181613

Keyword

nonn,base

Author

Tanya Khovanova, Jan 30 2011

Extensions

a(8)-a(11) from Robert G. Wilson v, Jan 30 2011

a(12)-a(24) from Hiroaki Yamanouchi, Mar 21 2015

Status

approved