A083736 Pseudoprimes to bases 2,5 and 7.

561, 29341, 46657, 75361, 115921, 162401, 252601, 294409, 314821, 334153, 340561, 399001, 410041, 488881, 512461, 530881, 552721, 656601, 658801, 710533, 721801, 852841, 1024651, 1141141, 1152271, 1168513, 1193221, 1461241, 1569457, 1615681

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..8691 (terms 1..81 from R. J. Mathar)

F. Richman, Primality testing with Fermat's little theorem

Formula

a(n) = n-th positive integer k(>1) such that 2^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).

Example

a(1)=561 since it is the first number such that 2^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).

Mathematica

Select[Range[1, 10^5, 2], CompositeQ[#] &&  PowerMod[2, #-1, #] == PowerMod[5, #-1, #] == PowerMod[7, #-1, #] == 1&] (* Amiram Eldar, Jun 29 2019 *)

Crossrefs

Intersection of A083732 and A005938. Intersection of A083733 and A005936. - R. J. Mathar, Apr 05 2011

Sequence in context: A232761 A232755 A264214 * A182090 A006931 A258801

Adjacent sequences: A083733 A083734 A083735 * A083737 A083738 A083739

Keyword

easy,nonn

Author

Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003

Status

approved