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 A256777 Primes of form n^2 + 625. 14

%I

%S 641,661,769,821,881,1109,1201,1301,1409,2069,2389,2741,3329,3541,

%T 3761,3989,4721,6101,6709,7349,7681,8369,9461,12289,14081,14549,16001,

%U 18049,19121,20789,25589,28181,31601,32309,33749,35221,35969,37489,38261,39041,39829

%N Primes of form n^2 + 625.

%C Conjecture: sequence is infinite.

%H Reinhard Zumkeller, <a href="/A256777/b256777.txt">Table of n, a(n) for n = 1..10000</a>

%o a256777 n = a256777_list !! (n-1)

%o a256777_list = [x | x <- map (+ 625) a000290_list, a010051' x == 1]

%o (PARI) list(lim)=if(lim<641,return([])); my(v=List(),t); forstep(n=4, sqrtint(lim\1-625), 2, if(isprime(t=n^2+625), listput(v,t))); Vec(v) \\ _Charles R Greathouse IV_, Aug 18 2017

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

%Y Primes of form n^2+b^4, b fixed: A002496 (b=1), A243451 (b=2), A256775 (b=3), A256776 (b=4), 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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