

A058383


Primes of form 1+(2^a)*(3^b), a>0, b>0.


15



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

1,1


COMMENTS

Prime numbers n such that cos(2*Pi/n) is an algebraic number of a 3smooth degree, but not a 2smooth degree.  Artur Jasinski, Dec 13 2006
From Antonio M. OllerMarcén, Sep 24 2009: (Start)
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)
Primes in A005109 but not in A092506.  R. J. Mathar, Sep 28 2012


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

1+A033845(n) is prime


MATHEMATICA

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 *)


CROSSREFS

Cf. A033845, A000423, A125866.
Sequence in context: A040034 A176229 A110074 * A005471 A249381 A040096
Adjacent sequences: A058380 A058381 A058382 * A058384 A058385 A058386


KEYWORD

nonn


AUTHOR

Labos Elemer, Dec 20 2000


STATUS

approved



