A102634 Numbers k such that 2^k + 13 is prime.

2, 4, 8, 20, 38, 64, 80, 292, 1132, 4108, 19934, 125278, 175628, 282184

Offset: 1

Author

Lei Zhou, Jan 20 2005

Keywords

• nonn
• hard
• more

Comments

If k is odd, then 2^k + 13 is divisible by 3. - Robert G. Wilson v, Jan 24 2005

a(15) > 5*10^5. - Robert Price, Aug 15 2015

For k in this sequence, the number 2^(k-1)*(2^k+13) has deficiency 14, cf. A141550. - M. F. Hasler, Jul 18 2016

Examples

			2^2+13 = 17 is prime.
2^4+13 = 29 is prime.
2^3+13 = 21 is not prime.
		

Links

• H. Lifchitz and R. Lifchitz (Editors), PRP Top Records, of the form 2^n+13.
• Lei Zhou, Between 2^n and primes [broken link].

Crossrefs

Cf. A019434 (2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), A057196 (2^k+9), A102633 (2^k+11), A102634 (this), A057197 (2^k+15), A057200 (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23).

Programs

Mathematica

Do[m = n; If[PrimeQ[2^n + 13], Print[n]], {n, 2, 19125, 2}] (* Robert G. Wilson v, Jan 24 2005 *)

PARI

first(m)=my(v=vector(m),r=1);for(i=1,m,while(!isprime(2^r + 13),r++);v[i]=r;r++);v; \\ Anders Hellström, Aug 15 2015

Formula

a(n) = 2*A253772(n). - Elmo R. Oliveira, Nov 12 2023

Extensions

a(10) from Robert G. Wilson v, Jan 24 2005

a(11)-a(14) from Robert Price, Aug 15 2015