|
%I #53 Jun 26 2020 06:21:12
%S 83,2593,194483,388963,31505923,57289763,96059603,99574273,169869313,
%T 276922883,395254163,414720001,3264481603,5125781251,6059221283,
%U 18233242723,35888419873,82012500001,135304020001,154550410643,159004011043,186320859203,206710354243,364488705443
%N Primes prime(k) such that 2*(prime(k)^2 - prime(k-1)^2) is a fourth power.
%C This is a subset of A335410.
%H David A. Corneth, <a href="/A332615/b332615.txt">Table of n, a(n) for n = 1..10000</a> (first 102 terms from Chai Wah Wu)
%e Prime(23)=83. Prime(22)=79. 2*(83^2 - 79^2) = 6^4.
%e Prime(378)=2593. Prime(377)=2591. 2*(2593^2 - 2591^2) = 12^4.
%t Select[Prime@Range[2, 500000], IntegerQ@Sqrt[Sqrt[2(#^2 - NextPrime[#, -1]^2)]]&] (* a modification of _Giovanni Resta_'s program for A335410 *)
%o (PARI) isok(p) = isprime(p) && ispower(2*(p^2-precprime(p-1)^2), 4); \\ _Michel Marcus_, Jun 08 2020
%o (PARI) lista(nn) = {my(pp=2); forprime(p=3, nn, if (ispower(2*(p^2 - pp^2), 4), print1(p, ", ")); pp = p;);} \\ _Michel Marcus_, Jun 08 2020
%Y Cf. A001248, A335410.
%K nonn
%O 1,1
%A _Jeff Brown_, Jun 08 2020
%E More terms from _Amiram Eldar_, Jun 08 2020
%E More terms from _Giovanni Resta_, Jun 08 2020
|
