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A334163 Primes p whose continued fraction expansion of sqrt(p) has a 1 in the second position.

%I A334163 #29 Sep 06 2022 00:32:20
%S A334163 3,7,13,23,31,43,47,59,61,73,79,97,113,137,139,157,163,167,191,193,
%T A334163 211,223,241,251,277,281,283,307,311,313,317,347,349,353,359,383,389,
%U A334163 397,421,431,433,439,463,467,479,509,521,523,557,563,569,571,601,607,613,617,619
%N A334163 Primes p whose continued fraction expansion of sqrt(p) has a 1 in the second position.
%C A334163 These are the primes that are located between an oblong number and its following square number. - _Charles Kusniec_, Apr 17 2020
%C A334163 Primes in A063657. - _Charles Kusniec_, Sep 04 2022
%H A334163 Robert Israel, <a href="/A334163/b334163.txt">Table of n, a(n) for n = 1..10000</a>
%p A334163 3,seq(op(select(isprime, [$(t^2+t+1)..(t^2+2*t-1)])),t=1..31); # _Robert Israel_, Apr 20 2020
%t A334163 Select[Range[1000], PrimeQ[#] && ContinuedFraction[Sqrt[#]][[2,1]] == 1 &] (* _Amiram Eldar_, Apr 17 2020 *)
%t A334163 Select[Prime[Range[150]],ContinuedFraction[Sqrt[#]][[2,1]]==1&] (* _Harvey P. Dale_, Mar 04 2022 *)
%o A334163 (PARI) isok(p) = isprime(p) && contfrac(sqrt(p))[2] == 1;
%Y A334163 Complement of A307508 with respect to the primes.
%Y A334163 Cf. A063657.
%K A334163 nonn
%O A334163 1,1
%A A334163 _Michel Marcus_, Apr 17 2020