A215343 -id:A215343 - cp's OEIS frontend

A216667 Semiprime 2-pseudoprimes of the form 10k + 7.

1387, 2047, 3277, 7957, 13747, 23377, 31417, 60787, 65077, 88357, 164737, 188057, 233017, 275887, 390937, 486737, 489997, 514447, 580337, 604117, 672487, 680627, 769567, 769757, 916327, 1092547, 1132657, 1145257, 1252697, 1293337, 1433407, 1493857, 1530787

Offset: 1

Marius Coman, Sep 13 2012

nonn

A very interesting observation due to Peter Bala: about half of the terms from the sequence have the form p*(4*p - 3), where p is prime. For this form of Fermat pseudoprimes see the sequences A213812 and A215343.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Poulet Number

Subsequence of A214305.

Cf. A001567.

list(lim)=my(v=List(),t); forprime(p=3,sqrtint(lim\=1), forprime(q=p+2,lim\p, t=p*q; if(t%10==7 && Mod(2,t)^t==2, listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Jun 30 2017

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

Original entry on oeis.org

348161, 831405, 1246785, 1275681, 2077545, 2513841, 5977153, 9613297, 13333441, 13823601, 18137505, 19523505, 21474181, 21880801, 37695505, 38171953, 44521301, 47734141, 54448153, 72887585, 75151441, 95423329

Offset: 1

Marius Coman, Oct 12 2012

nonn

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

Eric Weisstein's World of Mathematics, Poulet Number

Cf. A001567, A213812, A215343.

cp's OEIS Frontend

A216667 Semiprime 2-pseudoprimes of the form 10k + 7.

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

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cp's OEIS Frontend

A216667 Semiprime 2-pseudoprimes of the form 10k + 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

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.

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