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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 (list; graph; refs; listen; history; text; internal format)
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 * A085635 A077434 A076136

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

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Last modified March 8 01:41 EST 2021. Contains 341934 sequences. (Running on oeis4.)