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A227136 Fermat pseudoprimes to base 2 which are not Euler pseudoprimes to base 2. 1
645, 1387, 2701, 2821, 4369, 4371, 7957, 8911, 11305, 13741, 13747, 13981, 14491, 18721, 19951, 23001, 23377, 30889, 31417, 31609, 35333, 39865, 41665, 55245, 57421, 60701, 60787, 63973, 68101, 72885, 83665, 88561, 91001, 93961, 101101, 107185, 121465 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These numbers can be factored by finding k = 2^((n-1)/2) mod n and taking gcd(k-1, n) and gcd(k+1, n). This is a special case of Kraitchik's method. - Charles R Greathouse IV, Dec 27 2013

Numbers n such that 2^(n-1) == 1 (mod n) and 2^((n-1)/2) != +-1 (mod n). - Thomas Ordowski, Feb 25 2016

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric W. Weisstein, MathWorld: Euler Pseudoprime

Eric W. Weisstein, MathWorld: Fermat Pseudoprime

MATHEMATICA

Select[Range[1000000], PowerMod[2, #-1, #] == 1 && ! PowerMod[2, (#-1)/2, #] == 1 && ! PowerMod[2, (#-1)/2, #] == # -1 &]

PROG

(PARI) is(n)=my(k=Mod(2, n)^(n\2)); k^2==1 && n%2 && k!=1 && k!=-1 \\ Charles R Greathouse IV, Dec 27 2013

CROSSREFS

Cf. A001567, A006970.

Sequence in context: A168626 A216023 A100873 * A216364 A063844 A265684

Adjacent sequences:  A227133 A227134 A227135 * A227137 A227138 A227139

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Jul 02 2013

STATUS

approved

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Last modified October 20 01:39 EDT 2018. Contains 316378 sequences. (Running on oeis4.)