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Revision History for A307453

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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.
(history; published version)

#18 by Bruno Berselli at Wed Apr 10 05:21:47 EDT 2019

STATUS

reviewed

approved

#17 by Joerg Arndt at Wed Apr 10 05:21:03 EDT 2019

STATUS

proposed

reviewed

#16 by Michel Marcus at Wed Apr 10 03:20:37 EDT 2019

STATUS

editing

proposed

#15 by Michel Marcus at Wed Apr 10 03:20:12 EDT 2019

EXAMPLE

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

CROSSREFS

Cf. A040000, A040001, A010121, A010129.

#14 by Michel Marcus at Wed Apr 10 03:18:29 EDT 2019

EXAMPLE

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

For p = 31, we have [5, ; 1, 1, 3, ...]; see A010129.

For p = 7, we have [2, ; 1, 1, 1, 4, ...]; see A010121.

STATUS

proposed

editing

#13 by Chai Wah Wu at Tue Apr 09 11:24:34 EDT 2019

STATUS

editing

proposed

#12 by Chai Wah Wu at Tue Apr 09 11:20:41 EDT 2019

DATA

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

OFFSET

1,0,1

EXTENSIONS

a(0) added by Chai Wah Wu, Apr 09 2019

STATUS

reviewed

editing

#11 by Michel Marcus at Tue Apr 09 10:57:57 EDT 2019

STATUS

proposed

reviewed

#10 by Daniel Suteu at Tue Apr 09 10:13:56 EDT 2019

STATUS

editing

proposed

#9 by Daniel Suteu at Tue Apr 09 10:11:57 EDT 2019

DATA

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

FORMULA

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

KEYWORD

nonn,more,new

EXTENSIONS

a(21)-a(29) from Daniel Suteu, Apr 09 2019

STATUS

approved

editing