This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A062073 Decimal expansion of Fibonacci factorial constant. 31
 1, 2, 2, 6, 7, 4, 2, 0, 1, 0, 7, 2, 0, 3, 5, 3, 2, 4, 4, 4, 1, 7, 6, 3, 0, 2, 3, 0, 4, 5, 5, 3, 6, 1, 6, 5, 5, 8, 7, 1, 4, 0, 9, 6, 9, 0, 4, 4, 0, 2, 5, 0, 4, 1, 9, 6, 4, 3, 2, 9, 7, 3, 0, 1, 2, 1, 4, 0, 2, 2, 1, 3, 8, 3, 1, 5, 3, 1, 2, 1, 6, 8, 4, 5, 2, 6, 2, 1, 5, 6, 2, 4, 9, 4, 7, 9, 7, 7, 4, 1, 2, 5, 9, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Fibonacci factorial constant is associated with the Fibonacci factorial A003266. Two closely related constants are A194159 and A194160. [Johannes W. Meijer, Aug 21 2011] REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.5. R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison Wesley, 1990, pp. 478, 571. LINKS Harry J. Smith, Table of n, a(n) for n=1..5000 M. Griffiths, Symmetric rational expressions in the Fibonacci numbers, Fib. Q., 46/47 (2008/2009), 262-267. [N. J. A. Sloane, Dec 05 2009] Simon Plouffe, Fibonacci factorials Eric Weisstein's World of Mathematics, Fibonacci Factorial Constant FORMULA C = (1-a)*(1-a^2)*(1-a^3)... 1.2267420... where a = -1/phi^2 and where phi is the Golden ratio = 1/2 + sqrt(5)/2. C = QPochhammer[ -1/GoldenRatio^2]. [Eric W. Weisstein, Dec 01 2009] C = A194159 * A194160. [Johannes W. Meijer, Aug 21 2011] C = exp( Sum_{k>=1} 1/(k*(1-(-(3+sqrt(5))/2)^k)) ). - Vaclav Kotesovec, Jun 08 2013 C = Sum_{k = -inf .. inf} (-1)^((k-1)*k/2) / phi^((3*k-1)*k), where phi = (1 + sqrt(5))/2. - Vladimir Reshetnikov, Sep 20 2016 EXAMPLE 1.226742010720353244417630230455361655871409690440250419643297301214... MATHEMATICA RealDigits[N[QPochhammer[-1/GoldenRatio^2], 105]][[1]] (* Alonso del Arte, Dec 20 2010 *) RealDigits[N[Re[(-1)^(1/24) * GoldenRatio^(1/12) / 2^(1/3) * EllipticThetaPrime[1, 0, -I/GoldenRatio]^(1/3)], 120]][[1]] (* Vaclav Kotesovec, Jul 19 2015, after Eric W. Weisstein *) PROG (PARI) \p 1300 a=-1/(1/2+sqrt(5)/2)^2; prod(n=1, 17000, (1-a^n)) (PARI) { default(realprecision, 5080); p=-1/(1/2 + sqrt(5)/2)^2; x=prodinf(k=1, 1-p^k); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b062073.txt", n, " ", d)) } \\ Harry J. Smith, Jul 31 2009 CROSSREFS Cf. A003266, A003267, A003268, A056569, A062072, A062381, A135407, A181926. Cf. A218490, A253924, A256831, A259314, A259405. Sequence in context: A174789 A210865 A210861 * A021445 A011145 A177852 Adjacent sequences:  A062070 A062071 A062072 * A062074 A062075 A062076 KEYWORD easy,nonn,cons AUTHOR Jason Earls, Jun 27 2001 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 December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)