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A175625 Numbers n such that gcd(n, 6) = 1, 2^(n-1) == 1 (mod n), and 2^(n-3) == 1 (mod (n-1)/2). 2
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 536870911, 46912496118443, 192153584101141163, with no other composites below 2^64 (the first two were found by 'venco' from the dxdy.ru forum). Many composite members of this sequence are of the form (2^k + 1)/3, starting with k = 47, 59, 83, 107, 179, 227, 263, 359, 383, ..., with 112 such k below 10000. 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

STATUS

approved

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Last modified March 26 16:31 EDT 2017. Contains 284137 sequences.