A307453 - OEIS

A307453

a(n) is the least prime p for which the continued fraction expansion of sqrt(p) has exactly n consecutive 1's starting at position 2.

2, 3, 31, 7, 13, 3797, 5273, 4987, 90371, 79873, 2081, 111301, 1258027, 5325101, 12564317, 9477889, 47370431, 709669249, 1529640443, 2196104969, 392143681, 8216809361, 30739072339, 200758317433, 370949963971, 161356959383, 1788677860531, 7049166342469, 4484287435283, 3690992602753

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..29.

Piotr Miska, Maciej Ulas, On consecutive 1's in continued fractions expansions of square roots of prime numbers, arXiv:1904.03404 [math.NT], 2019. See Table 1 p. 15.

Index entries for continued fractions for constants

FORMULA

Limit_{n->infinity} (sqrt(a(n)) - floor(sqrt(a(n)))) = A094214. - Daniel Suteu, Apr 09 2019

EXAMPLE

For p = 2, we have [1; 2, ...]; see A040000.

For p = 3, we have [1; 1, 2, ...]; see A040001.