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A138929 Twice the prime powers A000961. 7
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 (list; graph; refs; listen; history; text; internal format)
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

From Peter Luschny, Aug 12 2009: (Start)

a := n -> `if`(1>=nops(numtheory[factorset](n)), 2*n, NULL):

seq(a(i), i=1..192); (End)

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: A022292 A225241 A087370 * A180081 A242418 A191146

Adjacent sequences:  A138926 A138927 A138928 * A138930 A138931 A138932

KEYWORD

nonn

AUTHOR

M. F. Hasler, Apr 04 2008

STATUS

approved

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Last modified April 25 10:11 EDT 2017. Contains 285379 sequences.