A339945 Numbers y such that sqrt(6*y^2+10)-3 is prime.

3, 13, 31, 129, 29180479, 121378881, 110778874246369293, 263631110418336671, 95129083120198558843838970225921, 213007829848951141529011991896053267187

Offset

1,1

Comments

sqrt(p + (p^2-1)/6) for p in A339935.

Primes in this sequence include 3, 13, 31. Are there any others?

Links

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

Example

a(3) = 31 is a term because sqrt(6*31^2+10)-3 = 73 is prime.

Maple

g:= gfun:-rectoproc({a(i+4)-10*a(i+2)+a(i)=0, a(0)=1, a(1)=3, a(2)=13, a(3)= 31}, a(i), remember):
select(y -> isprime(sqrt(6*y^2+10)-3), map(g, [$1..100]));

Crossrefs

Cf. A339935.

Sequence in context: A213970 A034050 A107689 * A154834 A159047 A219971

Adjacent sequences: A339942 A339943 A339944 * A339946 A339947 A339948

Keyword

nonn

Author

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

Status

approved