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.

13, 2, 127, 19, 211, 463, 919, 1741, 1951, 2539, 4861, 8521, 8719, 9811, 10651, 21319, 25309, 19609, 29527, 42379, 61879, 58171, 89959, 97579, 144271, 135319, 164431, 217519, 201919, 230101, 216451, 289111, 307759, 323359, 558979, 468199, 488791

Offset: 1

Author

Zak Seidov, Mar 08 2011

Keywords

• nonn

Comments

Version of A187261 for prime numbers.

a(n) >= A187261(n) and a(n) = A187261(n) if A187261(n) is prime.

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,..

Among first 100 terms, the largest is a(96)=48169339, less than this there are also a(102)=44302171 and a(105)=47106151.

Examples

			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.
a(2) = 2 because the c.f. of sqrt(2) = 1,{2}, and c.f. contains 1..2.
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.
a(4) = 19 because the c.f. of sqrt(19) = 4, {2, 1, 3, 1, 2, 8}, and c.f. contains 1..4.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A187261.