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

1,2

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?

Links

Table of n, a(n) for n=1..48.

Prog

(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( c<n, m++; c += prod(x=1, m-1, !isprime( lift( Mod(x, m)^4 ) ) ) ); m)}; /* Michael Somos, Jan 07 2011 */

Crossrefs

A065428 (x^2 mod n).

Sequence in context: A053021 A122700 A048486 * A065428 A059747 A254328

Adjacent sequences: A179399 A179400 A179401 * A179403 A179404 A179405

Keyword

nonn

Author

Joerg Arndt, Jan 07 2011

Status

approved