A256775 Primes of the form n^2 + 81.

97, 181, 277, 337, 757, 1237, 2017, 3217, 4177, 5557, 5857, 6481, 7477, 11317, 13537, 16981, 19681, 21397, 33937, 37717, 48481, 51157, 52981, 59617, 62581, 65617, 80737, 84181, 87697, 96181, 102481, 106357, 111637, 119797, 144481, 149077, 155317, 160081

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

subsequence of A045349.

Cf. A010051, A000290; subsequence of A028916.

Primes of form n^2+b^4, b fixed: A002496 (b=1), A243451 (b=2), A256776 (b=4), A256777 (b=5), A256834 (b=6), A256835 (b=7), A256836 (b=8), A256837 (b=9), A256838 (b=10), A256839 (b=11), A256840 (b=12), A256841 (b=13).

Programs

Haskell

a256775 n = a256775_list !! (n-1)
a256775_list = [x | x <- map (+ 81) a000290_list, a010051' x == 1]

Magma

[p: p in PrimesUpTo(200000)| IsSquare(p-81)]; // Vincenzo Librandi, Apr 20 2015

Mathematica

Select[Range[400]^2 + 81, PrimeQ] (* Michael De Vlieger, Apr 19 2015 *)

PARI

for(n=1,10^3,if(isprime(p=n^2+81),print1(p,", "))) \\ Derek Orr, Apr 24 2015