The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A140654 Numerators of convergents to transcendental number defined by Yun Gao and Jining Gao. 0
 3, 201, 52690971, 949196149445558443966545, 5549006906251488336142058083587971135417862217678366680875041864474951923 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Gao and Gao prove in Example 7, on p.11, that the series converges to a transcendental number. LINKS Table of n, a(n) for n=1..5. Yun Gao and Jining Gao, Some sufficient conditions of a given series with rational terms converging to an irrational number, arXiv:0807.1376 FORMULA a(n) = numerator of SUM[k=1..n] (3^n)/(2^3^n). EXAMPLE a(1)/denom = (3^1)/(2^3^1) = 3/8. a(2)/denom = (3/8) + (3^2)/(2^3^2) = (3/8)+(9/512) = 201/512. a(3)/denom = 201/512 + (3^3)/(2^3^3) = 201/512 + 27/(2^27)= 52690971/134217728. a(4)/denom = 52690971/134217728 + (3^4)/(2^3^4) = 52690971/134217728 + 81/(2^81) = (3/8) + (9/512) + (27/(2^27)) + (81/(2^81)) = 949196149445558443966545/2417851639229258349412352. a(5)/denom = (3/8) + (9/512) + (27/(227)) + (81/(281)) + (243/(2243)) = 5549006906251488336142058083587971135417862217678366680875041864474951923/ 14134776518227074636666380005943348126619871175004951664972849610340958208 = 0 + 1/2+ 1/1+ 1/1+ 1/4+ 1/1+ 1/3+ 1/1+ 1/3+ 1/18+ 1/1+ 1/2+ 1/3+ 1/13+ 1/1+ 1/4+ 1/6+ 1/2+ 1/1+ 1/1657008+ 1/3+ 1/3+ 1/2+ 1/4+ 1/1+ 1/4+ 1/1+ 1/1+ 1/1+ 1/1+ 1/1+ 1/7+ 1/1+ 1/1+ 1/40+ 1/3+ 1/8+ 1/3+ 1/7+ 1/2+ 1/2+ 1/9.9500067e+21+ 1/1+ 1/1+ 1/2+ 1/3+ 1/1+ 1/9+ 1/3+ 1/2+ 1/4+ 1/3+ 1/2+ 1/1+ 1/1+ 1/1+ 1/1+ 1/1+ 1/13+ 1/2+ 1/1+ 1/2+ 1/1+ 1/1+ 1/1+ 1/1+ 1/1+ 1/2+ 1/2+ 1/1+ 1/2+ 1/2+ 1/184111+ 1/1+ 1/2+ 1/4+ 1/1+ 1/14+ 1/4+ 1/1+ 1/1+ 1/2+ 1/1+ 1/2+ 1/3+ 1/27+ 1/15+ 1/1+ 1/1+ 1/5+ 1/1+ 1/49+ 1/2+ 1/2, to give the continued fraction for the last example. CROSSREFS Sequence in context: A342578 A264674 A306630 * A229602 A080297 A080274 Adjacent sequences: A140651 A140652 A140653 * A140655 A140656 A140657 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Jul 09 2008 STATUS approved

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

Last modified December 6 22:36 EST 2023. Contains 367616 sequences. (Running on oeis4.)