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 5-digit 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 k-digit 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
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