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

Author

Amiram Eldar, Jan 26 2018

Keywords

• nonn

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.

Crossrefs

Subsequence of A001567.

Cf. A005382, A217465, A303447, A303448.

Programs

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 *)

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