A307508 - OEIS

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

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OFFSET

1,1

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

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.