A083738 Pseudoprimes to bases 2,3 and 7.

1105, 2465, 10585, 18721, 29341, 46657, 75361, 104653, 115921, 162401, 226801, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461, 530881, 534061, 552721, 574561, 658801, 721801, 852841, 1024651

Offset: 1

Author

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

Keywords

• easy
• nonn

Examples

			a(1)=1105 since it is the first number such that 2^(k-1) = 1 (mod k), 3^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10460 (terms 1..98 from R. J. Mathar)
• F. Richman, Primality testing with Fermat's little theorem

Crossrefs

Intersection of A001567 and A083735. Intersection of A005935 and A083733. - R. J. Mathar, Apr 05 2011

Programs

Mathematica

Select[Range[1, 10^5, 2], CompositeQ[#] &&  PowerMod[2, #-1,#] == PowerMod[3, #-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), 3^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).