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

1,1

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

Prog

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

Crossrefs

Subsequence of A001567; A001262 is a subsequence.

Sequence in context: A342902 A112140 A044883 * A154717 A306478 A051388

Adjacent sequences: A288150 A288151 A288152 * A288154 A288155 A288156

Keyword

nonn

Author

Charles R Greathouse IV, Jun 05 2017

Status

approved