A020503 -id:A020503 - cp's OEIS frontend

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

M. F. Hasler, Apr 03 2008

nonn

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

Robert Price, Table of n, a(n) for n = 1..49
Yves Gallot, Cyclotomic polynomials and prime numbers

Cf. A020503, A138920-A138940.

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

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

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

cp's OEIS Frontend

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

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