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A138926
Indices k such that A020503(k)=Phi[k](-4) is prime, where Phi is a cyclotomic polynomial.
2
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
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Apr 03 2008
EXTENSIONS
a(36)-a(49) from Robert Price, Apr 07 2012
STATUS
approved