A083735 Pseudoprimes to bases 3 and 7.

703, 1105, 2465, 10585, 18721, 19345, 29341, 38503, 46657, 50881, 75361, 76627, 88831, 104653, 115921, 146611, 162401, 188191, 213265, 226801, 252601, 278545, 286903, 294409, 314821, 334153, 340561, 359341, 385003, 385201, 399001, 410041

Offset: 1

Author

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

Keywords

• nonn

Examples

			a(1)=703 since it is the first number such that 3^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..16479 (terms 1..151 from R. J. Mathar)
• F. Richman, Primality testing with Fermat's little theorem
• Index entries for sequences related to pseudoprimes

Crossrefs

Intersection of A005935 and A005938. - R. J. Mathar, Apr 05 2011

Programs

Mathematica

Select[Range[420000],!PrimeQ[#]&&PowerMod[3,#-1,#]==1&&PowerMod[7,#-1,#] == 1&] (* Harvey P. Dale, Mar 08 2014 *)

PARI

is(n)=!isprime(n)&&Mod(7,n)^(n-1)==1&&Mod(3,n)^(n-1)==1 \\ Charles R Greathouse IV, Apr 12 2012

Formula

a(n) = n-th positive integer k(>1) such that 3^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).