A138934 Indices k such that A019322(k) = Phi[k](4) is prime, where Phi is a cyclotomic polynomial.

1, 2, 4, 6, 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

1,2

Comments

It appears that except for 1,2 and 6, all terms of this sequence are multiples 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 13 2012

Second comment is true; this follows from applying Theorem 1.1 in the Gallot paper with p = 2 and m even. - Charlie Neder, May 16 2019

Links

Robert Price, Table of n, a(n) for n = 1..51

Yves Gallot, Cyclotomic polynomials and prime numbers

Index entries for cyclotomic polynomials, values at X

Mathematica

Select[Range[1000], PrimeQ[Cyclotomic[#, 4]] &]

Prog

(PARI) for( i=1, 999, ispseudoprime( polcyclo(i, 4)) && print1( i", "))

Crossrefs

Cf. A019322, A072226, A138920-A138940.

Sequence in context: A185976 A117146 A061553 * A008764 A228354 A065386

Adjacent sequences: A138931 A138932 A138933 * A138935 A138936 A138937

Keyword

nonn

Author

M. F. Hasler, Apr 03 2008

Extensions

a(29)-a(51) from Robert Price, Apr 12 2012

Status

approved