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

1,1

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A035852 A214486 A045146 * A161021 A283521 A334010

Adjacent sequences: A083732 A083733 A083734 * A083736 A083737 A083738

Keyword

nonn

Author

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

Status

approved