A334163 Primes p whose continued fraction expansion of sqrt(p) has a 1 in the second position.

3, 7, 13, 23, 31, 43, 47, 59, 61, 73, 79, 97, 113, 137, 139, 157, 163, 167, 191, 193, 211, 223, 241, 251, 277, 281, 283, 307, 311, 313, 317, 347, 349, 353, 359, 383, 389, 397, 421, 431, 433, 439, 463, 467, 479, 509, 521, 523, 557, 563, 569, 571, 601, 607, 613, 617, 619

Offset: 1

Author

Michel Marcus, Apr 17 2020

Keywords

• nonn

Comments

These are the primes that are located between an oblong number and its following square number. - Charles Kusniec, Apr 17 2020

Primes in A063657. - Charles Kusniec, Sep 04 2022

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A307508 with respect to the primes.

Cf. A063657.

Programs

Maple

3,seq(op(select(isprime, [$(t^2+t+1)..(t^2+2*t-1)])),t=1..31); # Robert Israel, Apr 20 2020

Mathematica

Select[Range[1000], PrimeQ[#] && ContinuedFraction[Sqrt[#]][[2,1]] == 1 &] (* Amiram Eldar, Apr 17 2020 *)
Select[Prime[Range[150]],ContinuedFraction[Sqrt[#]][[2,1]]==1&] (* Harvey P. Dale, Mar 04 2022 *)

PARI

isok(p) = isprime(p) && contfrac(sqrt(p))[2] == 1;