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A138934
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Indices k such that A019322(k)=Phi[k](4) is prime, where Phi is a cyclotomic polynomial.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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
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MATHEMATICA
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Select[Range[1000], PrimeQ[Cyclotomic[#, 4]] &]
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PROG
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(PARI) for( i=1, 999, ispseudoprime( polcyclo(i, 4)) && print1( i", ")) /* use ...subst(polcyclo(i), x, 4)... in PARI < 2.4.2 */
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CROSSREFS
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Cf. A019322, A072226, A138920-A138940.
Sequence in context: A185976 A117146 A061553 * A008764 A065386 A048951
Adjacent sequences: A138931 A138932 A138933 * A138935 A138936 A138937
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler, Apr 03 2008
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EXTENSIONS
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a(29)-a(51) from Robert Price, Apr 12 2012
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STATUS
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approved
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