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A186884 Numbers k such that 2^(k-1) == 1 + b*k (mod k^2), where b divides k - 2^p for some integer p >= 0 and 2^p <= b. 0

%I #22 Aug 20 2023 16:56:13

%S 3,5,7,11,13,17,19,29,31,37,71,127,173,199,233,251,257,379,491,613,

%T 881,2047,2633,2659,3373,3457,5501,5683,8191,11497,13249,15823,16879,

%U 18839,22669,24763,25037,26893,30139,45337,48473,56671,58921,65537,70687,74531,74597,77023,79669,87211,92237,102407,131071,133493,181421,184511,237379,250583,254491,281381

%N Numbers k such that 2^(k-1) == 1 + b*k (mod k^2), where b divides k - 2^p for some integer p >= 0 and 2^p <= b.

%C This sequence contains A186645 as a subsequence (corresponding to p=0).

%C All composites in this sequence are 2-pseudoprimes, A001567. This sequence contains all terms of A054723. Another composite term is 4294967297 = 2^32 + 1, which does not belong to A054723. In other words, all known composite terms have the form (2^x + 1) or (2^x - 1). Are there composites not of this form?

%C This sequence contains all the primes of the forms (2^x + 1) and (2^x - 1), i.e., subsequences A092506 and A000668.

%K nonn

%O 1,1

%A _Alzhekeyev Ascar M_, Feb 28 2011

%E Edited by _Max Alekseyev_, Mar 14 2011

%E a(25) and a(26) interchanged by _Georg Fischer_, Jul 08 2022

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)