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

%I A307508 #47 Aug 29 2024 03:06:28
%S A307508 2,5,11,17,19,29,37,41,53,67,71,83,89,101,103,107,109,127,131,149,151,
%T A307508 173,179,181,197,199,227,229,233,239,257,263,269,271,293,331,337,367,
%U A307508 373,379,401,409,419,443,449,457,461,487,491,499,503,541,547,577,587,593,599
%N A307508 Primes p for which the continued fraction expansion of sqrt(p) does not have a 1 in the second position.
%C A307508 These are the primes that are located between a square number and the following oblong number. - _Charles Kusniec_, Apr 17 2020
%C A307508 Primes in A063656. - _Charles Kusniec_, Sep 04 2022
%H A307508 Michel Marcus, <a href="/A307508/b307508.txt">Table of n, a(n) for n = 1..5000</a>
%H A307508 Piotr Miska and Maciej Ulas, <a href="https://doi.org/10.1080/10586458.2019.1605319">On consecutive 1's in continued fractions expansions of square roots of prime numbers</a>, Experimental Mathematics, 31:1 (2022), 238-251. Also <a href="https://arxiv.org/abs/1904.03404">arXiv:1904.03404</a> [math.NT], 2019.
%H A307508 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e A307508 For p = 2,  we have [1; 2, ...]; see A040000.
%e A307508 For p = 5,  we have [2; 4, ...]; see A040002.
%e A307508 For p = 11, we have [3; 3, ...]; see A040007.
%o A307508 (PARI) isok(p) = isprime(p) && contfrac(sqrt(p))[2] != 1;
%Y A307508 Cf. A040000, A040002, A040007, A067614, A307453, A063656.
%Y A307508 Complement of A334163 with respect to the primes.
%K A307508 nonn
%O A307508 1,1
%A A307508 _Michel Marcus_, Apr 11 2019