A083736 - OEIS

%I #18 Jun 29 2019 08:33:16

%S 561,29341,46657,75361,115921,162401,252601,294409,314821,334153,

%T 340561,399001,410041,488881,512461,530881,552721,656601,658801,

%U 710533,721801,852841,1024651,1141141,1152271,1168513,1193221,1461241,1569457,1615681

%N Pseudoprimes to bases 2,5 and 7.

%H Amiram Eldar, <a href="/A083736/b083736.txt">Table of n, a(n) for n = 1..8691</a> (terms 1..81 from R. J. Mathar)

%H F. Richman, <a href="http://math.fau.edu/Richman/carm.htm">Primality testing with Fermat's little theorem</a>

%F a(n) = n-th positive integer k(>1) such that 2^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).

%e a(1)=561 since it is the first number such that 2^(k-1) = 1 (mod k), 5^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).

%t Select[Range[1, 10^5, 2], CompositeQ[#] &&  PowerMod[2, #-1,#] == PowerMod[5, #-1,#] == PowerMod[7, #-1,#] == 1&] (* _Amiram Eldar_, Jun 29 2019 *)

%Y Intersection of A083732 and A005938. Intersection of A083733 and A005936. - _R. J. Mathar_, Apr 05 2011

%K easy,nonn

%O 1,1

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