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

1,1

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Intersection of A005935 and A005936.

Sequence in context: A200429 A092717 A203134 * A137598 A252966 A133560

Adjacent sequences: A083731 A083732 A083733 * A083735 A083736 A083737

Keyword

easy,nonn

Author

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

Status

approved