A307508 Primes p for which the continued fraction expansion of sqrt(p) does not have a 1 in the second position.

2, 5, 11, 17, 19, 29, 37, 41, 53, 67, 71, 83, 89, 101, 103, 107, 109, 127, 131, 149, 151, 173, 179, 181, 197, 199, 227, 229, 233, 239, 257, 263, 269, 271, 293, 331, 337, 367, 373, 379, 401, 409, 419, 443, 449, 457, 461, 487, 491, 499, 503, 541, 547, 577, 587, 593, 599

Offset

1,1

Comments

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

Primes in A063656. - Charles Kusniec, Sep 04 2022

Links

Michel Marcus, Table of n, a(n) for n = 1..5000

Piotr Miska and Maciej Ulas, On consecutive 1's in continued fractions expansions of square roots of prime numbers, Experimental Mathematics, 31:1 (2022), 238-251. Also arXiv:1904.03404 [math.NT], 2019.

Index entries for continued fractions for constants

Example

For p = 2,  we have [1; 2, ...]; see A040000.
For p = 5,  we have [2; 4, ...]; see A040002.
For p = 11, we have [3; 3, ...]; see A040007.

Prog

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

Crossrefs

Cf. A040000, A040002, A040007, A067614, A307453, A063656.

Complement of A334163 with respect to the primes.

Sequence in context: A080165 A239712 A224363 * A063535 A091653 A088348

Adjacent sequences: A307505 A307506 A307507 * A307509 A307510 A307511

Keyword

nonn

Author

Michel Marcus, Apr 11 2019

Status

approved