

A095810


Numbers of the form 2^j (mod 10^k), where j >= 0 and k >= 1, with leading zeros suppressed.


5



1, 2, 4, 6, 8, 12, 16, 24, 28, 32, 36, 44, 48, 52, 56, 64, 68, 72, 76, 84, 88, 92, 96, 104, 112, 128, 136, 144, 152, 168, 176, 184, 192, 208, 216, 224, 232, 248, 256, 264, 272, 288, 296, 304, 312, 328, 336, 344, 352, 368, 376, 384, 392, 408, 416, 424, 432, 448
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OFFSET

1,2


COMMENTS

Given only the last 5 (say) digits of a large integer N, can you determine whether N is not some power of 2? This is equivalent to ask which 5digit numbers are of the form 2^j (mod 10^6) where j is any positive integer. So if the last 5 digits of N are not in this sequence, then N is not a power of 2.
If we have only the last k digits of an integer N, we can determine whether N is not a power of 2, if and only if the number given by those digits is divisible by 5 OR not a multiple of 2^k.  Francisco Salinas (franciscodesalinas(AT)hotmail.com), Aug 27 2004. [Edited for clarification and simplification by M. F. Hasler, Nov 06 2017, following discussions with David A. Corneth, Peter Munn and N. J. A. Sloane. The given condition says when a kdigit number is not in this sequence. In that case we know that N is not a power of 2, otherwise, we cannot know.]


LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000


MATHEMATICA

Take[ Union[ Flatten[ Table[ PowerMod[2, j, 10^k], {j, 0, 100}, {k, 3}]]], 58] (* Robert G. Wilson v, Sep 11 2004 *)


PROG

(PARI) is(n) = valuation(n, 2)>=#digits(n)&&valuation(n, 5)==0 \\ David A. Corneth, Oct 17 2017
(PARI) nxt(n) = if(n==1, return(2)); q = #digits(n); n += 2^q; while(n%5==0, n += 2^q); n \\ David A. Corneth, Oct 17 2017


CROSSREFS

Cf. A097574, A113022, A113023.
Sequence in context: A058629 A323508 A324850 * A025487 A333964 A279537
Adjacent sequences: A095807 A095808 A095809 * A095811 A095812 A095813


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Aug 30 2004


EXTENSIONS

Additional comments from Robert G. Wilson v, Oct 11 2005
Edited by M. F. Hasler, Nov 06 2017


STATUS

approved



