login
Pseudoprimes to bases 2,3 and 7.
1

%I #18 Jun 29 2019 08:33:41

%S 1105,2465,10585,18721,29341,46657,75361,104653,115921,162401,226801,

%T 252601,278545,294409,314821,334153,340561,399001,410041,449065,

%U 488881,512461,530881,534061,552721,574561,658801,721801,852841,1024651

%N Pseudoprimes to bases 2,3 and 7.

%H Amiram Eldar, <a href="/A083738/b083738.txt">Table of n, a(n) for n = 1..10460</a> (terms 1..98 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), 3^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).

%e a(1)=1105 since it is the first number such that 2^(k-1) = 1 (mod k), 3^(k-1) = 1 (mod k) and 7^(k-1) = 1 (mod k).

%t Select[Range[1, 10^5, 2], CompositeQ[#] && PowerMod[2, #-1,#] == PowerMod[3, #-1,#] == PowerMod[7, #-1,#] == 1&] (* _Amiram Eldar_, Jun 29 2019 *)

%Y Intersection of A001567 and A083735. Intersection of A005935 and A083733. - _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