A138929 Twice the prime powers A000961.

2, 4, 6, 8, 10, 14, 16, 18, 22, 26, 32, 34, 38, 46, 50, 54, 58, 62, 64, 74, 82, 86, 94, 98, 106, 118, 122, 128, 134, 142, 146, 158, 162, 166, 178, 194, 202, 206, 214, 218, 226, 242, 250, 254, 256, 262, 274, 278, 298, 302, 314, 326, 334, 338, 346, 358, 362, 382

Offset

1,1

Comments

Except for the initial term a(1)=2, indices k such that A020513(k)=Phi[k](-1) is prime, where Phi is a cyclotomic polynomial.

This is illustrated by the PARI code, although it is probably more efficient to calculate a(n) as 2*A000961(n).

{ a(n)/2 ; n>1 } are also the indices for which A020500(k)=Phi[k](1) is prime.

A188666(k) = A000961(k+1) for k: a(k) <= k < a(k+1), k > 0;

A188666(a(n)) = A000961(n+1). [Reinhard Zumkeller, Apr 25 2011]

Links

Table of n, a(n) for n=1..58.

Index entries for cyclotomic polynomials, values at X

Formula

A138929(n) = 2*A000961(n).

A138929 = {2} union { k | Phi[k](-1)=A020513(k) is prime } = {2} union { 2k | Phi[k](1)=A020500(k) is prime }.

Maple

a := n -> `if`(1>=nops(numtheory[factorset](n)), 2*n, NULL):
seq(a(i), i=1..192); # Peter Luschny, Aug 12 2009

Mathematica

Select[ Range[3, 1000], PrimeQ[ Cyclotomic[#, -1]] &] (* Robert G. Wilson v, Mar 25 2012 *)

Prog

(PARI) print1(2); for( i=1, 999, isprime( polcyclo(i, -1)) & print1(", ", i)) /* use ...subst(polcyclo(i), x, -2)... in PARI < 2.4.2. It should be more efficient to calculate a(n) as 2*A000961(n) ! */

Crossrefs

Cf. A000961, A020513, A138920-A138940. A230078 (complement).

Sequence in context: A225241 A087370 A364158 * A334169 A180081 A340854

Adjacent sequences: A138926 A138927 A138928 * A138930 A138931 A138932

Keyword

nonn

Author

M. F. Hasler, Apr 04 2008

Status

approved