

A095810


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


4



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



