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 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 (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 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 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

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)