A230076 - OEIS

A230076

a(n) = (A007521(n)-1)/4.

1, 3, 7, 9, 13, 15, 25, 27, 37, 39, 43, 45, 49, 57, 67, 69, 73, 79, 87, 93, 97, 99, 105, 115, 127, 135, 139, 153, 163, 165, 169, 175, 177, 183, 189, 193, 199, 205, 207, 213, 219, 235, 249, 253, 255, 265, 267, 273, 277, 279, 295, 303, 307

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OFFSET

1,2

COMMENTS

Because A007521(n) are the primes congruent 5 (mod 8) it is clear that a(n) is congruent 1 (mod 2), that is odd.

2*a(n) = A055034(A007521(n)), the degree of the minimal polynomial C(A007521(n), x) of 2*rho(Pi/A007521(n)) (see A187360).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = (A007521(n)-1)/4.

EXAMPLE

The minimal polynomial C(A007521(2), x) = C(13, x) has degree 6 = 2*a(2) because C(13, x) = x^6 - x^5 - 5*x^4 + 4*x^3 + 6*x^2 - 3*x -1.

MATHEMATICA

(Select[8*Range[0, 200] + 5, PrimeQ] - 1)/4 (* Amiram Eldar, Jun 08 2022 *)

CROSSREFS

Cf. A007521, A055034, A187360, 4*A005123 (1 (mod 8) case), A186287 (3 (mod 8) case), A186302 (7 (mod 8) case).

Sequence in context: A258011 A000959 A204085 * A120226 A137310 A118567

Adjacent sequences: A230073 A230074 A230075 * A230077 A230078 A230079

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 24 2013

STATUS

approved