A152913 - OEIS

%I #23 Sep 29 2023 12:11:36

%S 17,97,337,881,3697,10657,16561,49297,66977,89041,149057,847601,

%T 988417,1146097,1972097,2522257,2836961,3553777,3959297,4398577,

%U 5385761,7166897,11073217,17653681,32530177,41532497,44048497,55272097,61627201

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

%C Also primes in A008514.

%C 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.

%H Vincenzo Librandi, <a href="/A152913/b152913.txt">Table of n, a(n) for n = 1..5000</a>

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

%t 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 *)

%t Select[Table[n^4+(n+1)^4,{n,0,700}],PrimeQ]

%t Select[Total/@Partition[Range[100]^4,2,1],PrimeQ] (* _Harvey P. Dale_, Sep 29 2023 *)

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

%Y Cf. A155211, A008514.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Dec 15 2008

%E Edited and extended by _Klaus Brockhaus_, Dec 21 2008