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

1,1

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

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 *)

Prog

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

Crossrefs

Complement of A307508 with respect to the primes.

Cf. A063657.

Sequence in context: A173196 A081662 A091652 * A291546 A134197 A053001

Adjacent sequences: A334160 A334161 A334162 * A334164 A334165 A334166

Keyword

nonn

Author

Michel Marcus, Apr 17 2020

Status

approved