A256836 Primes of form n^2 + 4096.

4177, 4217, 4457, 4721, 4937, 6121, 7121, 7577, 7817, 9137, 9721, 10337, 10657, 11321, 12377, 13121, 15121, 16417, 17321, 18257, 23417, 23977, 25121, 26297, 31321, 34721, 36137, 36857, 38321, 40577, 44497, 47777, 50321, 52057, 52937, 54721, 57457, 81937

Offset: 1

Author

Reinhard Zumkeller, Apr 11 2015

Keywords

• nonn

Comments

Conjecture: sequence is infinite.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010051, A000290; subsequence of A028916.

Primes of form n^2+b^4, b fixed: A002496 (b=1), A243451 (b=2), A256775 (b=3), A256776 (b=4), A256777 (b=5), A256834 (b=6), A256835 (b=7), A256837 (b=9), A256838 (b=10), A256839 (b=11), A256840 (b=12), A256841 (b=13).

Programs

Haskell

a256836 n = a256836_list !! (n-1)
a256836_list = [x | x <- map (+ 4096) a000290_list, a010051' x == 1]

Mathematica

Select[Range[1,300,2]^2+4096,PrimeQ] (* Harvey P. Dale, May 26 2025 *)