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%I #24 Mar 10 2019 01:43:31
%S 2,4,6,8,10,14,16,18,22,26,32,34,38,46,50,54,58,62,64,74,82,86,94,98,
%T 106,118,122,128,134,142,146,158,162,166,178,194,202,206,214,218,226,
%U 242,250,254,256,262,274,278,298,302,314,326,334,338,346,358,362,382
%N Twice the prime powers A000961.
%C 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.
%C This is illustrated by the PARI code, although it is probably more efficient to calculate a(n) as 2*A000961(n).
%C { a(n)/2 ; n>1 } are also the indices for which A020500(k)=Phi[k](1) is prime.
%C A188666(k) = A000961(k+1) for k: a(k) <= k < a(k+1), k > 0;
%C A188666(a(n)) = A000961(n+1). [_Reinhard Zumkeller_, Apr 25 2011]
%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index entries for cyclotomic polynomials, values at X</a>
%F A138929(n) = 2*A000961(n).
%F A138929 = {2} union { k | Phi[k](-1)=A020513(k) is prime } = {2} union { 2k | Phi[k](1)=A020500(k) is prime }.
%p a := n -> `if`(1>=nops(numtheory[factorset](n)),2*n,NULL):
%p seq(a(i),i=1..192); # _Peter Luschny_, Aug 12 2009
%t Select[ Range[3, 1000], PrimeQ[ Cyclotomic[#, -1]] &] (* _Robert G. Wilson v_, Mar 25 2012 *)
%o (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) ! */
%Y Cf. A000961, A020513, A138920-A138940. A230078 (complement).
%K nonn
%O 1,1
%A _M. F. Hasler_, Apr 04 2008
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