A105330 Numbers n such that 2^(n+1)+2n+1 is prime.

0, 1, 2, 3, 4, 7, 10, 13, 14, 26, 40, 49, 50, 110, 142, 170, 315, 349, 502, 842, 1251, 1630, 2054, 2906, 3482, 5110, 5227, 5620, 8224, 8788, 8912, 13027, 16243, 17222, 28557, 46532, 54974, 92866, 93093, 120855, 155416

Offset: 1

Author

Farideh Firoozbakht, Apr 28 2005

Keywords

• more
• nonn

Comments

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.

No other n < 10^5. -T. D. Noe, Jun 23 2008

No other n < 300000. - T. D. Noe, Apr 03 2009

Examples

			110 is in the sequence because 2^111+2*110+1=2596148429267413814265248164610269 is prime.
		

Crossrefs

Cf. A083874, A105331.

Programs

Mathematica

Do[If[PrimeQ[2^(m + 1) + 2m + 1], Print[m]], {m, 0, 30500}]

PARI

is(n)=isprime(2^(n+1)+2*n+1) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

4 more terms from T. D. Noe, Jun 23 2008

Added two more terms -- T. D. Noe, Apr 03 2009