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

3, 5, 7, 11, 13, 17, 19, 37, 41, 67, 73, 97, 131, 137, 193, 257, 521, 577, 641, 769, 1033, 1153, 2053, 2081, 2113, 4099, 4129, 8209, 12289, 16417, 18433, 32771, 32801, 32833, 40961, 65537, 65539, 133121, 147457, 163841, 262147, 262153, 262657

Offset: 1

Author

Benoit Cloitre, May 14 2002

Keywords

• easy
• nonn

Comments

This sequence is the union of A081091 and the Fermat primes, A000215. - T. D. Noe, Jun 22 2007

Odd primes with Hamming weight (A000120) at most three. - Jeppe Stig Nielsen, Dec 09 2020

Examples

			41 = 2^5 + 2^3 + 1, hence 41 is in the sequence.
		

Links

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

Crossrefs

Cf. A000215, A081091.

Cf. A000120.

Programs

Maple

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

Mathematica

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 *)
Union[Select[Total/@(2^#&/@Union[Sort[Tuples[Range[0,20],2]]])+1,PrimeQ]] (* Harvey P. Dale, Jun 06 2020 *)

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),",")))

Extensions

More terms from Sascha Kurz, Aug 15 2002