The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A298737 Numerators of successive rational approximations converging to 2*Pi from above for n >= 1, with a(-1) = 0 and a(0) = 1. 2
 0, 1, 7, 13, 19, 44, 377, 710, 104703, 208696, 312689, 2292816, 6565759, 10838702, 90982559, 171126416, 251270273, 331414130, 411557987, 2549491779, 14885392687, 56992078969, 99098765251, 141205451533, 183312137815, 225418824097, 267525510379, 309632196661, 351738882943, 393845569225, 435952255507 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 COMMENTS Suggested by Henry Baker in a message to the math-fun mailing list, Mar 16 2018. LINKS FORMULA Set a(-1) = 0; a(0) = 1; a(n+1) = c(n) * a(n) - a(n-1), where t(0) = 2*Pi, c(n) = ceiling (t(n)), and t(n+1) = 1/(c(n) - t(n)). EXAMPLE The best integer over-estimate of 2*Pi is 7. Between 2*Pi and 7 the rational with the smallest denominator is 13/2. Between 2*Pi and 13/2, the rational with the smallest denominator is 19/3. So a(1) = 7, a(2) = 13, a(3) = 19. CROSSREFS Cf. A046995, a similar sequence of numerators of rationals converging to 2*Pi, the traditional continued fraction convergents. For the c sequence see A299922, and for the denominators see A299923. Sequence in context: A040096 A181938 A073648 * A109558 A108106 A231506 Adjacent sequences:  A298734 A298735 A298736 * A298738 A298739 A298740 KEYWORD frac,nonn AUTHOR Allan C. Wechsler, Mar 18 2018 EXTENSIONS Offset corrected by Altug Alkan, Mar 19 2018 More terms from Altug Alkan and N. J. A. Sloane (independently), Mar 19 2018 a(-1) = 0 prepended by Altug Alkan, Mar 26 2018 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 May 18 18:29 EDT 2021. Contains 343998 sequences. (Running on oeis4.)