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

Author

Michel Marcus, Apr 11 2019

Keywords

• nonn

Comments

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

Primes in A063656. - Charles Kusniec, Sep 04 2022

Examples

			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.
		

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

Crossrefs

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

Complement of A334163 with respect to the primes.

Programs

PARI

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