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

1,1

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.

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.

Example

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

Crossrefs

Cf. A001567, A006935, A057942.

Sequence in context: A236977 A108162 A270973 * A296117 A176770 A038681

Adjacent sequences: A287294 A287295 A287296 * A287298 A287299 A287300

Keyword

nonn

Author

Amiram Eldar, May 26 2017

Status

approved