A061119 Primes in the sequence n^2 + 2^n (A001580).

3, 17, 593, 32993, 2097593, 8589935681

Offset: 1

Author

Amarnath Murthy, Apr 21 2001

Keywords

• nonn

Comments

p and p^2 + 2^p are both prime only for p=3. All positive n satisfy the congruence n=3 (mod 6). - Lekraj Beedassy, Sep 07 2004

For values of n, see A064539. - Lekraj Beedassy, Jan 01 2007

The next term has 605 digits. - Harvey P. Dale, Jul 19 2017

Examples

			a(3) = 593 = 2^9 + 9^2.
a(4) = 32993 = 2^15 + 15^2.
		

References

• J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 165 pp. 30; 160, Ellipses Paris 2004.

Crossrefs

Subsequence of A094133.

Cf. A001580, A064539, A075896.

Programs

Mathematica

Select[Table[n^2+2^n,{n,1000}],PrimeQ] (* Harvey P. Dale, Jul 19 2017 *)

PARI

for(n=1,10^7, if(isprime(n^2+2^n),print(n^2+2^n)))

Formula

a(n) = A001580(A064539(n)). - Elmo R. Oliveira, Feb 18 2025

Extensions

More terms from Jason Earls, Aug 09 2001. Next term too large to include.