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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.
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
OFFSET
0,1
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.
For p = 31, we have [5; 1, 1, 3, ...]; see A010129.
For p = 7, we have [2; 1, 1, 1, 4, ...]; see A010121.
PROG
(PARI) isok(p, n) = {my(c=contfrac(sqrt(p))); for (k=2, n+1, if (c[k] != 1, return (0)); ); return(c[n+2] != 1); }
a(n) = {my(p=2); while (! isok(p, n), p = nextprime(p+1)); p; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 09 2019
EXTENSIONS
a(21)-a(29) from Daniel Suteu, Apr 09 2019
a(0) added by Chai Wah Wu, Apr 09 2019
STATUS
approved