A138926 Indices k such that A020503(k)=Phi[k](-4) is prime, where Phi is a cyclotomic polynomial.

3, 4, 8, 12, 16, 20, 28, 40, 60, 92, 96, 104, 140, 148, 156, 300, 356, 408, 596, 612, 692, 732, 756, 800, 952, 996, 1004, 1228, 1268, 2240, 2532, 3060, 3796, 3824, 3944, 5096, 5540, 7476, 7700, 8544, 9800, 14628, 15828, 16908, 18480, 20260, 21924, 24656, 38456

Offset

1,1

Comments

It appears that for all k>1, a(k) is a multiple of 4.

It also appears that all Cyclotomic Polynomials, Phi[k](x), where k is a multiple of 4 have no odd powers of x. For example, Phi[20](x)=x^8-x^6+x^4-x^2+1. This implies that Phi[k](x)=Phi[k](-x), where k is a multiple of 4. - Robert Price, Apr 14 2012

Links

Robert Price, Table of n, a(n) for n = 1..49

Yves Gallot, Cyclotomic polynomials and prime numbers

Mathematica

Select[ Range[3, 5000], PrimeQ[ Cyclotomic[#, -4]] &] (* Robert G. Wilson v, Mar 25 2012 *)

Prog

(PARI) for( i=1, 999, ispseudoprime( polcyclo(i, -4)) && print1( i", ")) /* use ...subst(polcyclo(i), x, -4)... in PARI < 2.4.2 */

Crossrefs

Cf. A020503, A138920-A138940.

Sequence in context: A293462 A190158 A188217 * A357501 A085635 A077434

Adjacent sequences: A138923 A138924 A138925 * A138927 A138928 A138929

Keyword

nonn

Author

M. F. Hasler, Apr 03 2008

Extensions

a(36)-a(49) from Robert Price, Apr 07 2012

Status

approved