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

1,1

Comments

This is a subset of A335410.

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A001248, A335410.

Sequence in context: A175662 A103233 A093283 * A156924 A084299 A017799

Adjacent sequences: A332612 A332613 A332614 * A332616 A332617 A332618

Keyword

nonn

Author

Jeff Brown, Jun 08 2020

Extensions

More terms from Amiram Eldar, Jun 08 2020

More terms from Giovanni Resta, Jun 08 2020

Status

approved