A332615 Primes prime(k) such that 2*(prime(k)^2 - prime(k-1)^2) is a fourth power.

83, 2593, 194483, 388963, 31505923, 57289763, 96059603, 99574273, 169869313, 276922883, 395254163, 414720001, 3264481603, 5125781251, 6059221283, 18233242723, 35888419873, 82012500001, 135304020001, 154550410643, 159004011043, 186320859203, 206710354243, 364488705443

Offset: 1

Author

Jeff Brown, Jun 08 2020

Keywords

• nonn

Comments

This is a subset of A335410.

Examples

			Prime(23)=83. Prime(22)=79. 2*(83^2 - 79^2) = 6^4.
Prime(378)=2593. Prime(377)=2591. 2*(2593^2 - 2591^2) = 12^4.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 102 terms from Chai Wah Wu)

Crossrefs

Cf. A001248, A335410.

Programs

Mathematica

Select[Prime@Range[2, 500000], IntegerQ@Sqrt[Sqrt[2(#^2 - NextPrime[#, -1]^2)]]&] (* a modification of Giovanni Resta's program for A335410 *)

PARI

isok(p) = isprime(p) && ispower(2*(p^2-precprime(p-1)^2), 4); \\ Michel Marcus, Jun 08 2020

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

Extensions

More terms from Amiram Eldar, Jun 08 2020

More terms from Giovanni Resta, Jun 08 2020