A185808 Least prime p such that the continued fraction expansion of its square root contains the first n natural numbers.

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

1,1

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.

Links

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

Example

a(1)=13  because the c.f. (c.f.=continued fraction) of sqrt(2) = 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(2) = 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, etc.

Crossrefs

Cf. A187261.

Sequence in context: A031066 A154355 A078421 * A178548 A098222 A114457

Adjacent sequences: A185805 A185806 A185807 * A185809 A185810 A185811

Keyword

nonn

Author

Zak Seidov, Mar 08 2011

Status

approved