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 A186645 Numbers k such that 2^(k-1) == 1 + b*k (mod k^2), where b divides k-1. 1
 3, 7, 11, 13, 19, 29, 31, 37, 71, 127, 379, 491, 2047, 2633, 2659, 3373, 8191, 13249, 26893, 70687, 74597, 87211, 131071, 184511, 524287, 642581, 1897121, 2676301, 2703739, 8388607, 15456151, 52368101, 102785339, 126233057, 193481677, 536870911, 856645921, 1552107133, 2001907169, 2147483647, 2935442621, 3668158729, 6004262437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All composites in this sequence are 2-pseudoprimes, A001567. The sequence contains all Mersenne numbers, A001348, k=2^p-1 for primes p (for which b=(k-1)/p). Correspondingly, the composites in this sequence contain all terms of A065341. The sequence also contains composites of the form 2^A001567(j) - 1, which do not belong to A065341. The existence of composites in the sequence that are not of the form 2^x-1 is unclear. The sequence contains A125854 as a subsequence. LINKS MAPLE isA186645 := proc(n)         if Power(2, n-1) mod n = 1 then                 x := Power(2, n-1) mod (n^2) ;                 b := (x-1)/n ;                 if b>0 then if modp(n-1, b) = 0 then true; else false; end if;                 else false;                 end if;         else                 false;         end if; end proc: for n from 1 do if isA186645(n) then printf("%d, \n", n); end if; end do: # R. J. Mathar, Mar 09 2011 CROSSREFS Cf. A001348, A001567, A125854. Sequence in context: A256863 A136087 A091250 * A077256 A341864 A067542 Adjacent sequences:  A186642 A186643 A186644 * A186646 A186647 A186648 KEYWORD nonn AUTHOR Alzhekeyev Ascar M, Feb 25 2011 EXTENSIONS Edited and more terms added by Max Alekseyev, Mar 14 2011 STATUS approved

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Last modified May 19 23:40 EDT 2022. Contains 353847 sequences. (Running on oeis4.)