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A058383
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Primes of form 1+(2^a)*(3^b), a>0, b>0.
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15
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7, 13, 19, 37, 73, 97, 109, 163, 193, 433, 487, 577, 769, 1153, 1297, 1459, 2593, 2917, 3457, 3889, 10369, 12289, 17497, 18433, 39367, 52489, 139969, 147457, 209953, 331777, 472393, 629857, 746497, 786433, 839809, 995329, 1179649, 1492993
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OFFSET
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1,1
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COMMENTS
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Prime numbers n such that cos(2pi/n) is an algebraic number of a 3-smooth degree, but not a 2-smooth degree. - Artur Jasinski, Dec 13 2006
Contribution from Antonio M. Oller-Marc\'en (oller(AT)unizar.es), Sep 24 2009: (Start)
In this case g.c.d.(a,b) is a power of 2.
A regular polygon of n sides is constructible by paper folding if and only if n=2^r3^sp_1...p_t with p_i being distinct primes of this kind. (End)
Primes in A005109 but not in A092506. - R. J. Mathar, Sep 28 2012
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
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FORMULA
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1+A033845(n) is prime
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MATHEMATICA
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Do[If[Take[FactorInteger[EulerPhi[2n + 1]][[ -1]], 1] == {3} && PrimeQ[2n + 1], Print[2n + 1]], {n, 1, 10000}] - Artur Jasinski, Dec 13 2006
mx = 1500000; s = Sort@ Flatten@ Table[1 + 2^j*3^k, {j, Log[2, mx]}, {k, Log[3, mx/2^j]}]; Select[s, PrimeQ] (* Robert G. Wilson v, Sep 28 2012 *)
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CROSSREFS
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Cf. A033845, A000423, A125866.
Sequence in context: A040034 A176229 A110074 * A005471 A040096 A181938
Adjacent sequences: A058380 A058381 A058382 * A058384 A058385 A058386
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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), Dec 20 2000
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STATUS
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approved
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