A335326 Lesser of 2 consecutive Fermat pseudoprimes to base 2 with no prime numbers in between them.

4369, 13741, 31609, 6973057, 208969201

Offset: 1

Author

Amiram Eldar, Jun 01 2020

Keywords

• nonn
• hard
• more

Comments

The corresponding larger counterparts are 4371, 13747, 31621, 6973063, 208969223.

The corresponding gaps between the consecutive pseudoprimes are 2, 6, 12, 6, 22.

a(6) > 10^15, if it exists.

Examples

			4369 is a term since it is a Fermat pseudoprime to base 2, and between it and the next Fermat pseudoprime to base 2, 4371, there is only one number, 4370, which is composite.
		

Crossrefs

Cf. A001567, A173619, A175736, A175737, A175738.

Programs

Mathematica

psp = Cases[Import["https://oeis.org/A001567/b001567.txt", "Table"], {, }][[;; , 2]]; s = {}; Do[If[NextPrime[psp[[k]]] > psp[[k + 1]], AppendTo[s, psp[[k]]]], {k, 1, Length[psp] - 1}]; s