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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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20
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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(2*Pi/n) is an algebraic number of a 3-smooth degree, but not a 2-smooth degree. - Artur Jasinski, Dec 13 2006
In this case gcd(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)
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LINKS
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FORMULA
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MAPLE
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N:= 10^10: # to get all terms <= N+1
sort(select(isprime, [seq(seq(1+2^a*3^b, a=1..ilog2(N/3^b)), b=1..floor(log[3](N)))])); # Robert Israel, Mar 02 2018
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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 *)
Select[Prime[Range[114000]], FactorInteger[#-1][[All, 1]]=={2, 3}&] (* Harvey P. Dale, Apr 13 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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