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Search: id:A061638
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| A061638 |
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Primes p such that the greatest prime divisor of p-1 is 7. |
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1
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| 29, 43, 71, 113, 127, 197, 211, 281, 337, 379, 421, 449, 491, 631, 673, 701, 757, 883, 1009, 1051, 1373, 1471, 2017, 2269, 2521, 2647, 2689, 2801, 3137, 3361, 3529, 4201, 4481, 5881, 6301, 7001, 7057, 7351, 7561, 7841, 8233, 8821, 10501, 10753, 12097
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Prime numbers n for which cos(2pi/n) is an algebraic number of 7-th degree. - Artur Jasinski (grafix(AT)csl.pl), Dec 13 2006
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,500
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FORMULA
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Primes of form (2^a)*(3^b)*(5^c)*(7^d)+1.
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EXAMPLE
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For n = {4, 8, 9, 12}, a(n)-1 = {70, 210, 280, 420} = 7*{10, 30, 40, 60}.
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MATHEMATICA
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Do[If[Take[FactorInteger[EulerPhi[2n + 1]][[ -1]], 1] == {7} && PrimeQ[2n + 1], Print[2n + 1]], {n, 1, 10000}] - Artur Jasinski (grafix(AT)csl.pl), Dec 13 2006
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PROGRAM
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(PARI) { default(primelimit, 108864001); n=0; forprime (p=3, 108864001, f=factor(p - 1)~; if (f[1, length(f)]==7, write("b061638.txt", n++, " ", p)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 25 2009]
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CROSSREFS
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The 4-th in a family of sequences after A019434(=Fermat-primes), A058383, A061599.
Cf. A019434, A058383, A023503, A034694, A006530, A006093, A035095, A061599.
Cf. A004729, A058383, A125867-A125875, A024899.
Sequence in context: A140444 A042969 A042967 this_sequence A136062 A039348 A043171
Adjacent sequences: A061635 A061636 A061637 this_sequence A061639 A061640 A061641
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 13 2001
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