A064539 Numbers n such that 2^n + n^2 is prime.

1, 3, 9, 15, 21, 33, 2007, 2127, 3759, 29355, 34653, 57285, 99069, 1933695

Offset: 1

Author

Jason Earls, Oct 16 2001

Keywords

• nonn
• more
• hard

Comments

Values 2^2007+2007^2, 2^2127+2127^2, 2^3759+3759^2 were proved prime with Primo.

n is always an odd multiple of 3 (except for the first term), i.e., a(n) is a subsequence of A016945. - Lekraj Beedassy, Jan 01 2007

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

References

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

Links

• Henri Lifchitz, Renaud Lifchitz, PRP Top Records. 2^n+n^2.

Crossrefs

Cf. A001580, A016945, A061119, A072180, A094133.

Programs

PARI

for(n=1,5000, if(isprime(2^n+n^2),print(n)))

Extensions

a(10)-a(13) from Hugo Pfoertner, Jun 26 2004

a(14) from Ryan Propper, May 11 2023. n=1933695 corresponds to a probable prime with 582101 digits, and was PRP tested with PFGW.