A152913 Primes of the form n^4 + (n+1)^4.

17, 97, 337, 881, 3697, 10657, 16561, 49297, 66977, 89041, 149057, 847601, 988417, 1146097, 1972097, 2522257, 2836961, 3553777, 3959297, 4398577, 5385761, 7166897, 11073217, 17653681, 32530177, 41532497, 44048497, 55272097, 61627201

Offset

1,1

Comments

Also primes in A008514.

Sequence is disjoint to A005385: If n^4 + (n+1)^4 is a prime p, then (p-1)/2 = n^4 + 2*n^3 + 3*n^2 + 2*n. (p-1)/2 = 8 for n = 1 and (p-1)/2 is divisible by n for n > 1. In each case, (p-1)/2 is not prime.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Example

For n=3, n^4 + (n+1)^4 = 337 is prime and (337-1)/2 = 168 = 3*56 is not prime.

Mathematica

f[n_]:=n^4+(n+1)^4; lst={}; Do[a=f[n]; If[PrimeQ[a], AppendTo[lst, a]], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 30 2009 *)
Select[Table[n^4+(n+1)^4, {n, 0, 700}], PrimeQ]
Select[Total/@Partition[Range[100]^4, 2, 1], PrimeQ] (* Harvey P. Dale, Sep 29 2023 *)

Prog

(Magma) [ a: n in [1..80] | IsPrime(a) where a is n^4+(n+1)^4 ];

Crossrefs

Cf. A155211, A008514.

Sequence in context: A103766 A165347 A008514 * A184327 A331877 A358572

Adjacent sequences: A152910 A152911 A152912 * A152914 A152915 A152916

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 15 2008

Extensions

Edited and extended by Klaus Brockhaus, Dec 21 2008

Status

approved