A302387 - OEIS

%I #26 May 08 2022 08:43:46

%S 3,3,3,5,3,3,3,179,169,935,663,8723,1481,2035,10199,18203,36395

%N a(n) is least number k >= 3 such that (k^(2^n) + (k-2)^(2^n))/2 is prime.

%H Henri Lifchitz & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=%2836395%5E65536%2B36393%5E65536%29%2F2&amp;action=Search">(36395^65536+36393^65536)/2</a>, a(16).

%e a(10)=663 corresponds to the prime (663^1024 + 661^1024)/2.

%t lst = {};  For[n=0, n<=14, n++, k=3;  While[! PrimeQ[(k^(2^n) + (k-2)^(2^n))/2], k++];  AppendTo[lst, k]];  lst (* _Robert Price_, Apr 29 2018 *)

%o (PARI) for(n=0,20,forstep(k=3,+oo,2,if(ispseudoprime((k^(2^n)+(k-2)^(2^n))/2),print1(k,", ");break())))

%Y Cf. A253633, A291944, A301738.

%K nonn,hard,more

%O 0,1

%A _Jeppe Stig Nielsen_, Apr 06 2018

%E a(15) from _Robert Price_, May 28 2018

%E a(16) from _Kellen Shenton_, Apr 14 2022