A339935 Primes p such that p+(p^2-1)/6 is a square.

5, 29, 73, 313, 71477281, 297316321, 271351716183549149, 645761700848255113, 233017713343294737292495403306881, 521760494347510297716737304478850311229

Offset

1,1

Comments

p + (p^2-1)/6 is the square of a prime for primes p = 5, 29 and 73. Are there any others?

Links

Robert Israel, Table of n, a(n) for n = 1..15

Example

a(3)=73 is a term because 73 is prime and 73+(73^2-1)/6 = 961 = 31^2 is a square.

Maple

f:= gfun:-rectoproc({a(i+4)-10*a(i+2)+a(i)=24, a(0)=1, a(1)=1, a(2)=5, a(3)=29}, a(i), remember):
select(isprime, map(f, [$1..100]));

Crossrefs

Cf. A339917, A339945.

Sequence in context: A224498 A087348 A154412 * A236075 A272650 A050409

Adjacent sequences: A339932 A339933 A339934 * A339936 A339937 A339938

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 23 2020

Status

approved