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

1,1

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

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).

Example

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).

Mathematica

Select[Range[1, 10^5, 2], CompositeQ[#] &&  PowerMod[2, #-1, #] == PowerMod[3, #-1, #] == PowerMod[7, #-1, #] == 1&] (* Amiram Eldar, Jun 29 2019 *)

Crossrefs

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

Sequence in context: A264498 A102924 A214017 * A265237 A355305 A291602

Adjacent sequences: A083735 A083736 A083737 * A083739 A083740 A083741

Keyword

easy,nonn

Author

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

Status

approved