A083734 Pseudoprimes to bases 3 and 5.

1541, 1729, 1891, 2821, 6601, 8911, 15841, 29341, 41041, 46657, 52633, 63973, 75361, 88831, 101101, 112141, 115921, 126217, 146611, 162401, 172081, 188461, 218791, 252601, 294409, 314821, 334153, 340561, 342271, 399001, 410041, 416641

Offset: 1

Author

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

Keywords

• easy
• nonn

Examples

			a(1)=1541 since it is the first nonprime number such that 3^(k-1) = 1 (mod k) and 5^(k-1) = 1 (mod k). - clarified by _Harvey P. Dale_, Jan 29 2013
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..15806 (terms 1..147 from R. J. Mathar)
• F. Richman, Primality testing with Fermat's little theorem

Crossrefs

Intersection of A005935 and A005936.

Programs

Mathematica

Select[Range[420000],!PrimeQ[#]&&PowerMod[3,#-1,#]==PowerMod[5,#-1,#]==1&] (* Harvey P. Dale, Jan 29 2013 *)

Formula

a(n) = n-th positive integer k(>1) such that 3^(k-1) = 1 (mod k) and 5^(k-1) = 1 (mod k).