

A287297


Fermat pseudoprimes n such that n+1 is prime.


2



161038, 9115426, 143742226, 665387746, 1105826338, 3434672242, 11675882626, 16732427362, 18411253246, 81473324626, 85898088046, 98730252226, 134744844466, 136767694402, 161097973246, 183689075122, 315554044786, 553588254766, 778581406786, 1077392692846
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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 n1 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. 5771.


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 A038681 A017285
Adjacent sequences: A287294 A287295 A287296 * A287298 A287299 A287300


KEYWORD

nonn


AUTHOR

Amiram Eldar, May 26 2017


STATUS

approved



