cp's OEIS Frontend

A070739 Primes of form 2^x + 2^y + 1.

%I A070739 #31 Dec 21 2020 07:33:25
%S A070739 3,5,7,11,13,17,19,37,41,67,73,97,131,137,193,257,521,577,641,769,
%T A070739 1033,1153,2053,2081,2113,4099,4129,8209,12289,16417,18433,32771,
%U A070739 32801,32833,40961,65537,65539,133121,147457,163841,262147,262153,262657
%N A070739 Primes of form 2^x + 2^y + 1.
%C A070739 This sequence is the union of A081091 and the Fermat primes, A000215. - _T. D. Noe_, Jun 22 2007
%C A070739 Odd primes with Hamming weight (A000120) at most three. - _Jeppe Stig Nielsen_, Dec 09 2020
%H A070739 T. D. Noe, <a href="/A070739/b070739.txt">Table of n, a(n) for n=1..1000</a>
%e A070739 41 = 2^5 + 2^3 + 1, hence 41 is in the sequence.
%p A070739 k := 0:for i from 1 to 140 do for j from i to 140 do if isprime(2^i+2^j+1) then k := k+1:c[k] := 2^i+2^j+1:fi:od:od:sort([3,seq(c[i],i=1..k)]);# gives all terms up to 2^140
%t A070739 f[x_,y_]:=2^x+2^y+1; imax=20; lst={}; Do[p=f[x,y]; If[p<2^imax+3 && PrimeQ[p], AppendTo[lst,p]], {y, 0, imax}, {x, 0, y}]; Union[lst] (* _Vladimir Joseph Stephan Orlovsky_, Apr 08 2011 *)
%t A070739 Union[Select[Total/@(2^#&/@Union[Sort[Tuples[Range[0,20],2]]])+1,PrimeQ]] (* _Harvey P. Dale_, Jun 06 2020 *)
%o A070739 (PARI) for(n=1,300,if(sum(i=0,n,sum(j=0,i,if(2^i+2^j+1-prime(n),0,1)))>0,print1(prime(n),",")))
%Y A070739 Cf. A000215, A081091.
%Y A070739 Cf. A000120.
%K A070739 easy,nonn
%O A070739 1,1
%A A070739 _Benoit Cloitre_, May 14 2002
%E A070739 More terms from _Sascha Kurz_, Aug 15 2002