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

1,1

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

Formula

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A321156 A227976 A224930 * A292367 A290805 A217465

Adjacent sequences: A083729 A083730 A083731 * A083733 A083734 A083735

Keyword

easy,nonn

Author

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

Status

approved