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 A256775 Primes of the form n^2 + 81. 14

%I

%S 97,181,277,337,757,1237,2017,3217,4177,5557,5857,6481,7477,11317,

%T 13537,16981,19681,21397,33937,37717,48481,51157,52981,59617,62581,

%U 65617,80737,84181,87697,96181,102481,106357,111637,119797,144481,149077,155317,160081

%N Primes of the form n^2 + 81.

%C Conjecture: sequence is infinite.

%H Reinhard Zumkeller, <a href="/A256775/b256775.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[400]^2 + 81, PrimeQ] (* _Michael De Vlieger_, Apr 19 2015 *)

%o a256775 n = a256775_list !! (n-1)

%o a256775_list = [x | x <- map (+ 81) a000290_list, a010051' x == 1]

%o (MAGMA) [p: p in PrimesUpTo(200000)| IsSquare(p-81)]; // _Vincenzo Librandi_, Apr 20 2015

%o (PARI) for(n=1,10^3,if(isprime(p=n^2+81),print1(p,", "))) \\ _Derek Orr_, Apr 24 2015

%Y subsequence of A045349.

%Y Cf. A010051, A000290; subsequence of A028916.

%Y 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).

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Apr 11 2015

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