A288153 - OEIS

%I #8 Jun 05 2017 21:27:03

%S 1729,1905,2047,2465,3277,4033,4681,8321,12801,15841,16705,18705,

%T 25761,29341,33153,34945,41041,42799,46657,49141,52633,65281,74665,

%U 75361,80581,85489,87249,88357,90751,104653,113201

%N Plumb pseudoprimes: odd composites that pass Colin Plumb's extended Euler criterion test.

%C Suppose n is composite. Then if n = 1 mod 8, it is in the sequence if 2^((n-1)/4) = 1 or -1 mod n; if n = 3 or 5 mod 8, it is in the sequence if 2^((n-1)/2) = -1 mod n; and if n = 3 mod 8, it is in the sequence if 2^((n-1)/2) = 1 mod n.

%C a(1) = 1729 is the Hardy-Ramanujan number. - _Omar E. Pol_, Jun 05 2017

%H Charles R Greathouse IV, <a href="/A288153/b288153.txt">Table of n, a(n) for n = 1..10000</a>

%o (Perl) use Math::Prime::Util ':all'

%o foroddcomposites { print "$_, " if is_euler_plumb_pseudoprime($_); } 9,999999;

%o (PARI) is(n)=if(n<2 || isprime(n) || n%2==0, return(0)); my(n8=n%8, e=n>>((n8==1)+1), t=Mod(2,n)^e); if(t==1, n8==1 || n8==7, if(t==-1, n8==1 || n8==3 || n8==5, 0))

%Y Subsequence of A001567; A001262 is a subsequence.

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Jun 05 2017