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A060215 Least a(n) such that the period of continued fraction for sqrt(a(n)) has at least n successive 1's. 2
2, 3, 7, 7, 13, 58, 58, 135, 461, 819, 2081, 13624, 13834, 35955, 95773, 244647, 639389, 1798800, 4374866, 11448871, 30002701, 78439683, 205337953, 541653136, 1407271538 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..24.

EXAMPLE

n  a(n)      C.f. period

0  2          1    2

1  3          2    1,2

2  7          4    1,1,1,4

3  7          4    1,1,1,4

4  13         5    1,1,1,1,6

5  58         7    1,1,1,1,1,1,14

6  58         7    1,1,1,1,1,1,14

7  135        8    1,1,1,1,1,1,1,22

8  461        15   2,8,10,1,1,1,1,1,1,1,1,10,8,2,42

9  819        10   1,1,1,1,1,1,1,1,1,56

10 2081       11   1,1,1,1,1,1,1,1,1,1,90

11 13624      62   1,2,1,...,4,5,1,1,1,1,1,1,1,1,1,1,1,5,4,...,1,2,1,232

12 13834      13   1,1,1,1,1,1,1,1,1,1,1,1,234

13 35955      14   1,1,1,1,1,1,1,1,1,1,1,1,1,378

14 95773      25   2,8,2,8,154,1,1,1,1,1,1,1,1,1,1,1,1,1,1,154,8,2,8,2,618

15 244647     16   1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,988

16 639389     17   1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1598

17 1798800    160  5,5,1,19,...,2,60,(17 1's),60,2,...,19,1,5,5,2682

18 4374866    19   1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4182

19 11448871   20   1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,6766

20 30002701   35   2,8,2,8,2,8,2738,(20 1's),738,8,2,8,2,8,2,10954

21 78439683   22   1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,17712

22 205337953  23   1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,28658

23 541653136  1442 2,3,1,...,4,581,(23 1's),581,4,...,1,3,2,46546

24 1407271538 25   1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,75026

MATHEMATICA

Table[Block[{k = 2}, While[NoneTrue[Map[Length, Select[If[IntegerQ@ #, {{#}}, Split@ Last@ ContinuedFraction@ #] &@ Sqrt@ k, First@ # == 1 &]], # >= n &], k++]; k], {n, 14}] (* Michael De Vlieger, Oct 26 2017 *)

PROG

(PARI) print1("2, 3, 7, "); n=3; for(k=1, 10^6, v=contfrac(sqrt(k)); s=0; for(l=1, length(v)-n, if(v[l]==1, s=s+1, s=0); if(s==n, print1(k", "); n=n+1; k=k-1; break)))

CROSSREFS

Cf. A071296.

Sequence in context: A171464 A276730 A179894 * A309666 A085420 A027672

Adjacent sequences:  A060212 A060213 A060214 * A060216 A060217 A060218

KEYWORD

nonn,more

AUTHOR

Jeff Burch, Mar 21 2001

EXTENSIONS

More terms from Ralf Stephan, Mar 26 2003

Definition clarified by T. D. Noe, Apr 07 2014

a(11), a(14) corrected and a(17)-a(23) added by Lars Blomberg, Oct 24 2015

a(0), a(24) from Chai Wah Wu, Sep 23 2019

STATUS

approved

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Last modified October 17 21:17 EDT 2021. Contains 348065 sequences. (Running on oeis4.)