A283004 Number of primes of the form n^4 + k^4 (A002645) with 1 <= k <= n.

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

Offset: 1

Author

Robert G. Wilson v and Altug Alkan, Feb 26 2017

Keywords

• nonn

Examples

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

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002645, A069004.

Programs

Mathematica

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]

PARI

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

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