A083732 Pseudoprimes to bases 2 and 5.

561, 1729, 2821, 5461, 6601, 8911, 12801, 13981, 15841, 29341, 41041, 46657, 52633, 63973, 68101, 75361, 101101, 113201, 115921, 126217, 137149, 162401, 172081, 188461, 252601, 294409, 314821, 334153, 340561, 399001, 401401, 410041, 488881

Offset: 1

Author

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

Keywords

• easy
• nonn

Examples

			a(1)=561 since 561 is the first positive integer k(>1) which satisfies 2^(k-1) = 1 (mod k) and 5^(k-1) = 1 (mod k).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..16699 (terms 1..169 from R. J. Mathar)
• F. Richman, Primality testing with Fermat's little theorem

Crossrefs

Intersection of A001567 and A005936. - R. J. Mathar, Apr 05 2011

Programs

Mathematica

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

PARI

lista(nn) = forcomposite(n=1, nn, if ((Mod(2, n)^(n-1)==1) && (Mod(5, n)^(n-1)==1), print1(n, ", "));); \\ Michel Marcus, Sep 08 2016

Formula

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