%I
%S 0,1,2,3,4,7,10,13,14,26,40,49,50,110,142,170,315,349,502,842,1251,
%T 1630,2054,2906,3482,5110,5227,5620,8224,8788,8912,13027,16243,17222,
%U 28557,46532,54974,92866,93093,120855,155416
%N Numbers n such that 2^(n+1)+2n+1 is prime.
%C If n is in the sequence & m=2^n*(2^(n+1)+2n+1) then sigma(m)+tau(m) =2m because sigma(m)=(2^(n+1)1)*(2^(n+1)+2n+2), tau(m)=2*(n+1) so sigma(m)+tau(m)=(2^(n+1)1)*(2^(n+1)+2n+2)+2*(n+1)=2m. Hence 2^A105330*(2^(A105330+1)+2*A105330+1) is a subsequence of A083874. A105331 is this subsequence. Next term is greater than 30500.
%C No other n < 10^5. _T. D. Noe_, Jun 23 2008
%C No other n < 300000.  _T. D. Noe_, Apr 03 2009
%e 110 is in the sequence because 2^111+2*110+1=2596148429267413814265248164610269 is prime.
%t Do[If[PrimeQ[2^(m + 1) + 2m + 1], Print[m]], {m, 0, 30500}]
%o (PARI) is(n)=isprime(2^(n+1)+2*n+1) \\ _Charles R Greathouse IV_, Feb 20 2017
%Y Cf. A083874, A105331.
%K more,nonn
%O 1,3
%A _Farideh Firoozbakht_, Apr 28 2005
%E 4 more terms from _T. D. Noe_, Jun 23 2008
%E Added two more terms  _T. D. Noe_, Apr 03 2009
