cp's OEIS Frontend

A185808 Least prime p such that the continued fraction expansion of its square root contains the first n natural numbers, but does not contain n+1.

%I A185808 #24 Oct 19 2024 08:33:44
%S A185808 13,2,127,19,211,463,919,1741,1951,2539,4861,8521,8719,9811,10651,
%T A185808 21319,25309,19609,29527,42379,61879,58171,89959,97579,144271,135319,
%U A185808 164431,217519,201919,230101,216451,289111,307759,323359,558979,468199,488791
%N A185808 Least prime p such that the continued fraction expansion of its square root contains the first n natural numbers, but does not contain n+1.
%C A185808 Version of A187261 for prime numbers.
%C A185808 a(n) >= A187261(n) and a(n) = A187261(n) if A187261(n) is prime.
%C A185808 a(n) = A187261(n) for n's: 2,4,5,6,9,14,15,16,18,19,20,22,23,24,25,26,27,28,29,30,31,33,..
%C A185808 Among first 100 terms, the largest is a(96)=48169339, less than this there are also a(102)=44302171 and a(105)=47106151.
%H A185808 Zak Seidov, <a href="/A185808/b185808.txt">Table of n, a(n) for n = 1..100</a>
%e A185808 a(1) = 13 because the c.f. (c.f.=continued fraction) of sqrt(13) = 3,{1,1,1,1,6}, and c.f. contains 1.
%e A185808 a(2) = 2 because the c.f. of sqrt(2) = 1,{2}, and c.f. contains 1..2.
%e A185808 a(3) = 127 because the c.f. of sqrt(127) = 11,{3,1,2,2,7,11,7,2,2,1,3,22}, and c.f. contains 1..3.
%e A185808 a(4) = 19 because the c.f. of sqrt(19) = 4, {2, 1, 3, 1, 2, 8}, and c.f. contains 1..4.
%Y A185808 Cf. A187261.
%K A185808 nonn
%O A185808 1,1
%A A185808 _Zak Seidov_, Mar 08 2011