This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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