

A152913


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


17



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
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OFFSET

1,1


COMMENTS

Also primes in A008514.
Sequence is disjoint to A005385: If n^4 + (n+1)^4 is a prime p, then (p1)/2 = n^4 + 2*n^3 + 3*n^2 + 2*n. (p1)/2 = 8 for n = 1 and (p1)/2 is divisible by n for n > 1. In each case, (p1)/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 (3371)/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]


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 A262207 A282997
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



