A287297 Fermat pseudoprimes n such that n+1 is prime.

161038, 9115426, 143742226, 665387746, 1105826338, 3434672242, 11675882626, 16732427362, 18411253246, 81473324626, 85898088046, 98730252226, 134744844466, 136767694402, 161097973246, 183689075122, 315554044786, 553588254766, 778581406786, 1077392692846

Offset: 1

Author

Amiram Eldar, May 26 2017

Keywords

• nonn

Comments

Kazimierz Szymiczek asked about the existence of such pseudoprimes in 1972 (Problem 42 in Rotkiewicz's book). Rotkiewicz found the first 6 terms. Rotkiewicz also proved that there is no Fermat pseudoprime n such that n-1 is prime.

Subsequence of A006935.

Examples

			161038 is in the sequence since it is a Fermat pseudoprime (2^161038 == 2 (mod 161038)), and 161038 + 1 = 161039 is prime.
		

References

• Andrzej Rotkiewicz, Pseudoprime Numbers and Their Generalizations, Student Association of the Faculty of Sciences, University of Novi Sad, Novi Sad, Yugoslavia, 1972.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..165
• Andrzej Rotkiewicz, On pseudoprimes having special forms and a solution of K. Szymiczek's problem, Acta Mathematica Universitatis Ostraviensis, Vol. 13, No. 1 (2005), pp. 57-71.

Crossrefs

Cf. A001567, A006935, A057942.