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A058383 Primes of form 1+(2^a)*(3^b), a>0, b>0.

%I A058383 #40 Aug 28 2020 01:50:24
%S A058383 7,13,19,37,73,97,109,163,193,433,487,577,769,1153,1297,1459,2593,
%T A058383 2917,3457,3889,10369,12289,17497,18433,39367,52489,139969,147457,
%U A058383 209953,331777,472393,629857,746497,786433,839809,995329,1179649,1492993
%N A058383 Primes of form 1+(2^a)*(3^b), a>0, b>0.
%C A058383 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
%C A058383 From _Antonio M. Oller-Marcén_, Sep 24 2009: (Start)
%C A058383 In this case gcd(a,b) is a power of 2.
%C A058383 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)
%C A058383 Primes in A005109 but not in A092506. - _R. J. Mathar_, Sep 28 2012
%C A058383 Conjecture: these are the only solutions >=7 to the equation A000010(x) + A000010(x-1) = floor((4*x-3)/3). - _Benoit Cloitre_, Mar 02 2018
%C A058383 These are also called Pierpont primes. - _Harvey P. Dale_, Apr 13 2019
%H A058383 Ray Chandler, <a href="/A058383/b058383.txt">Table of n, a(n) for n = 1..8378</a> (terms < 10^1000, first 1000 terms from T. D. Noe)
%F A058383 Primes of the form 1 + A033845(n).
%p A058383 N:= 10^10: # to get all terms <= N+1
%p A058383 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
%t A058383 Do[If[Take[FactorInteger[EulerPhi[2n + 1]][[ -1]],1] == {3} && PrimeQ[2n + 1], Print[2n + 1]], {n, 1, 10000}] (* _Artur Jasinski_, Dec 13 2006 *)
%t A058383 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 *)
%t A058383 Select[Prime[Range[114000]],FactorInteger[#-1][[All,1]]=={2,3}&] (* _Harvey P. Dale_, Apr 13 2019 *)
%Y A058383 Cf. A033845, A000423, A125866, A217035.
%K A058383 nonn
%O A058383 1,1
%A A058383 _Labos Elemer_, Dec 20 2000