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A217835 Fermat pseudoprimes to base 2 that can be written as p^2*n - p*n + p, where p is also a Fermat pseudoprime to base 2 and n is a positive integer. 0

%I

%S 348161,831405,1246785,1275681,2077545,2513841,5977153,9613297,

%T 13333441,13823601,18137505,19523505,21474181,21880801,37695505,

%U 38171953,44521301,47734141,54448153,72887585,75151441,95423329

%N Fermat pseudoprimes to base 2 that can be written as p^2*n - p*n + p, where p is also a Fermat pseudoprime to base 2 and n is a positive integer.

%C After a(22) = 95423329, no more terms through 10^8.

%C The corresponding (p,n): (341,3), (645,2), (645,3), (341,11), (645,5), (561,8), (1729,2), (1387,5), (341,120), (561,44), (1905,5), (645,47), (3277,2), (2701,3), (2047,9), (4369,2), (341,384), (2821,6), (2047,13), (2465,12), (3277,7), (4369,5).

%C Conjecture: For any Fermat pseudoprime p to base 2 there are infinitely many Fermat pseudoprimes to base 2 equal to p^2*n - p*n + p, where n is a positive integer.

%C See the sequence A215343: the generalized formula from there is p^2*n - p*n + p^2, which suggests an extrapolated formula for obtaining some Fermat pseudoprime to base 2 from another: p^2*n - p*n + p^k.

%C Conjecture: For any Fermat pseudoprime p to base 2 and any positive integer k, there are infinitely many Fermat pseudoprimes to base 2 equal to p^2*n - p*n + p^k, where n is a positive integer.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PouletNumber.html">Poulet Number</a>

%Y Cf. A001567, A213812, A215343.

%K nonn

%O 1,1

%A _Marius Coman_, Oct 12 2012

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Last modified September 26 22:53 EDT 2020. Contains 337377 sequences. (Running on oeis4.)