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

Author

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

Keywords

• easy
• nonn

Examples

			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).
		

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

Crossrefs

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

Programs

Mathematica

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

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).