A298758 Numbers k such that both k and 2k-1 are Poulet numbers (Fermat pseudoprimes to base 2).

15709, 65281, 20770621, 104484601, 112037185, 196049701, 425967301, 2593182901, 16923897871, 32548281361, 45812984491, 52035130951, 55897227751, 82907336737, 90003640021, 92010062101, 138016057141, 204082130071, 310026150211, 620006892121, 622333751509

Offset

1,1

Comments

2*a(n) - 1 = A303531(n) belongs to A217465. - Max Alekseyev, Apr 24 2018

Numbers k such that both k and 2k+1 are Poulet numbers are listed in A303447.

If p is a prime such that 2*p-1 is also a prime (A005382) and k = (2^(2*p-1)+1)/3 and 2*k-1 are both composites, then k is a term of this sequence (Rotkiewicz, 2000). - Amiram Eldar, Nov 09 2023

Links

Amiram Eldar, Table of n, a(n) for n = 1..3031 (terms below 2^64)

Andrzej Rotkiewicz, Arithmetic progressions formed by pseudoprimes, Acta Mathematica et Informatica Universitatis Ostraviensis, Vol. 8, No. 1 (2000), pp. 61-74.

Mathematica

s = Import["b001567.txt", "Data"][[All, -1]]; n = Length[s];
aQ[n_] := ! PrimeQ[n] && PowerMod[2, (n - 1), n] == 1;
a = {}; Do[p = 2*s[[k]] - 1; If[aQ[p], AppendTo[a, s[[k]]]], {k, 1, n}]; a (* using the b-File from A001567 *)

Prog

(PARI) isP(n) = (Mod(2, n)^n==2) && !isprime(n) && (n>1);
isok(n) = isP(n) && isP(2*n-1); \\ Michel Marcus, Mar 09 2018

Crossrefs

Subsequence of A001567.

Cf. A005382, A217465, A303447, A303448.

Sequence in context: A134121 A177949 A204728 * A205289 A205897 A350884

Adjacent sequences: A298755 A298756 A298757 * A298759 A298760 A298761

Keyword

nonn

Author

Amiram Eldar, Jan 26 2018

Status

approved