A288153 Plumb pseudoprimes: odd composites that pass Colin Plumb's extended Euler criterion test.

1729, 1905, 2047, 2465, 3277, 4033, 4681, 8321, 12801, 15841, 16705, 18705, 25761, 29341, 33153, 34945, 41041, 42799, 46657, 49141, 52633, 65281, 74665, 75361, 80581, 85489, 87249, 88357, 90751, 104653, 113201

Offset: 1

Author

Charles R Greathouse IV, Jun 05 2017

Keywords

• nonn

Comments

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.

a(1) = 1729 is the Hardy-Ramanujan number. - Omar E. Pol, Jun 05 2017

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A001567; A001262 is a subsequence.

Programs

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))

Perl

use Math::Prime::Util ':all'
foroddcomposites { print "$, " if is_euler_plumb_pseudoprime($); } 9,999999;