A283004 - OEIS

%I #11 Feb 27 2017 01:05:57

%S 1,1,1,2,2,1,3,2,2,2,3,0,3,2,2,4,4,3,6,4,2,2,5,5,3,7,3,5,5,5,2,6,3,10,

%T 3,5,8,5,6,4,9,6,9,3,6,9,8,4,6,8,7,6,13,8,6,7,5,7,9,4,8,14,3,7,7,6,7,

%U 10,9,4,14,5,10,13,5,10,9,6,14,6,8,12,11,7,13,10,14,9,15,7

%N Number of primes of the form n^4 + k^4 (A002645) with 1 <= k <= n.

%H Altug Alkan, <a href="/A283004/b283004.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 2 because 4^4 + 1^4 = 257 and 4^4 + 3^4 = 337 are prime numbers.

%t f[n_] := Block[{b = Mod[n, 2] + 1, c = 0}, While[b < n, If[ Mod[n^4 + b^4, 16] == 1 && PrimeQ[n^4 + b^4], c++]; b++]; c]; f[1] = 1; Array[f, 90]

%o (PARI) a(n) = if(n==1, 1, sum(k=1, n-1, isprime(n^4+k^4)));

%o (PARI) first(n)=my(v=vector(n),n4); for(N=1,n, n4=N^4; forstep(k=N%2+1,N,2, if(isprime(n4+k^4), v[N]++))); v[1]++; v \\ _Charles R Greathouse IV_, Feb 27 2017

%Y Cf. A002645, A069004.

%K nonn

%O 1,4

%A _Robert G. Wilson v_ and _Altug Alkan_, Feb 26 2017