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A175625
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Numbers n such that gcd(n, 6) = 1, 2^(n-1) == 1 (mod n), and 2^(n-3) == 1 (mod (n-1)/2).
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4
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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
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OFFSET
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1,1
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COMMENTS
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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 the form A007583(k)=(2^(2k+1) + 1)/3 for k 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.
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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PROG
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(PARI) isA175625(n) = gcd(n, 6)==1 && Mod(2, n)^(n-1)==1 && Mod(2, n\2)^(n-3)==1
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CROSSREFS
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Sequence in context: A089056 A210981 A255769 * A082496 A239733 A265768
Adjacent sequences: A175622 A175623 A175624 * A175626 A175627 A175628
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KEYWORD
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nonn
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AUTHOR
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Alzhekeyev Ascar M, Jul 28 2010, Jul 30 2010
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EXTENSIONS
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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
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STATUS
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approved
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