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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 (list; graph; refs; listen; history; text; internal format)
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.

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

Cf. A040000, A040001, A010121, A010129.

Sequence in context: A093712 A035514 A114009 * A143665 A074479 A272043

Adjacent sequences:  A307449 A307450 A307451 * A307454 A307455 A307456

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

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Last modified June 24 17:50 EDT 2019. Contains 324330 sequences. (Running on oeis4.)