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A332615 Primes prime(k) such that 2*(prime(k)^2 - prime(k-1)^2) is a fourth power. 2
83, 2593, 194483, 388963, 31505923, 57289763, 96059603, 99574273, 169869313, 276922883, 395254163, 414720001, 3264481603, 5125781251, 6059221283, 18233242723, 35888419873, 82012500001, 135304020001, 154550410643, 159004011043, 186320859203, 206710354243, 364488705443 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)