This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A096170 #33 Aug 07 2025 14:03:53 %S A096170 41,313,1201,7321,14281,41761,97241,139921,353641,750313,1156721, %T A096170 5278001,6922921,8925313,12705841,14199121,21523361,56275441,60775313, %U A096170 81523681,87450313,100266961,138461441,273990641,370600313,407865361 %N A096170 Primes of the form (k^4 + 1)/2. %C A096170 Note that k must be odd. Terms of primitive Pythagorean triples: (k^2, (k^4-1)/2, (k^4+1)/2). %H A096170 Charles R Greathouse IV, <a href="/A096170/b096170.txt">Table of n, a(n) for n = 1..10000</a> %e A096170 a(1)=41 because (3^4 + 1)/2 = 82/2 = 41 is prime. %t A096170 Select[(Range[200]^4+1)/2,PrimeQ] (* _Harvey P. Dale_, Mar 09 2013 *) %o A096170 (Magma) [ a: n in [0..2500] | IsPrime(a) where a is ((n^4+1) div 2) ]; // _Vincenzo Librandi_, Apr 15 2011 %o A096170 (PARI) list(lim)=my(v=List(),t); forstep(n=3,sqrtnint(lim\1*2-1,4),2, if(isprime(t=(n^4+1)/2), listput(v,t))); Vec(v) \\ _Charles R Greathouse IV_, Feb 14 2017 %Y A096170 Cf. A096169 (n^4+1)/2 is prime, A000068 n^4+1 is prime, A037896 primes of the form n^4+1, A096171 n^4+1 is an odd semiprime, A096172 largest prime factor of n^4+1. %K A096170 nonn %O A096170 1,1 %A A096170 _Hugo Pfoertner_, Jun 19 2004 %E A096170 Name edited by _Zak Seidov_, Apr 14 2011