A179402 Numbers n such that all x^4 mod n are nonprimes.

1, 2, 3, 4, 5, 8, 12, 15, 16, 24, 28, 30, 40, 48, 56, 60, 72, 80, 85, 88, 96, 104, 105, 112, 120, 140, 145, 160, 168, 232, 240, 255, 265, 280, 312, 408, 420, 520, 624, 680, 760, 840, 1040, 1320, 1360, 1848, 1904, 4080

Offset: 1

Author

Joerg Arndt, Jan 07 2011

Keywords

• nonn

Comments

A065428 is a subsequence.

No more such numbers up to 10^6.

Observe that many of these numbers are of the form k^2-1. Why?

Crossrefs

A065428 (x^2 mod n).

Programs

PARI

for(n=1,10^6,q=1;for(x=1,n-1,if(isprime(component(Mod(x,n)^4,2)),q=0;break()));if(q,print1(n,", ")));

PARI

{a(n) = my(c, m); if(n<=1, n==1, c=1; m=1; while( cMichael Somos, Jan 07 2011 */