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 A175625 Numbers k such that gcd(k, 6) = 1, 2^(k-1) == 1 (mod k), and 2^(k-3) == 1 (mod (k-1)/2). 4
 7, 11, 23, 31, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 683, 719, 839, 863, 887, 983, 1019, 1123, 1187, 1283, 1291, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2543 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All composites in this sequence are 2-pseudoprimes, A001567. That subsequence begins with 536870911, 46912496118443, 192153584101141163, with no other composites below 2^64 (the first two were found by 'venco' from the dxdy.ru forum), and contains the terms of A303448 that are not multiples of 3. Correspondingly, composite terms include those of the form A007583(m) = (2^(2m+1) + 1)/3 for m in A303009. The only known composite member not of this form is a(1018243) = 536870911. Intended as a pseudoprimality test; note that many primes do not pass the third condition either. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 PROG (PARI) isA175625(n) = gcd(n, 6)==1 && Mod(2, n)^(n-1)==1 && Mod(2, n\2)^(n-3)==1 CROSSREFS Sequence in context: A089056 A210981 A255769 * A082496 A239733 A265768 Adjacent sequences: A175622 A175623 A175624 * A175626 A175627 A175628 KEYWORD nonn AUTHOR Alzhekeyev Ascar M, Jul 28 2010, Jul 30 2010 EXTENSIONS Partially edited by N. J. A. Sloane, Jul 29 2010 Entry rewritten by Charles R Greathouse IV, Aug 04 2010 Comment and b-file from Charles R Greathouse IV, Sep 06 2010 Edited by Max Alekseyev, May 28 2014, Apr 24 2018 STATUS approved

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)