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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
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
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 February 24 16:16 EST 2024. Contains 370307 sequences. (Running on oeis4.)