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

 

Logo

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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A242208 Decimal expansion of log_2(phi), the logarithm to base 2 of phi, the "golden ratio" (1+sqrt(5))/2. 15
6, 9, 4, 2, 4, 1, 9, 1, 3, 6, 3, 0, 6, 1, 7, 3, 0, 1, 7, 3, 8, 7, 9, 0, 2, 6, 6, 8, 9, 8, 5, 9, 5, 2, 2, 3, 4, 6, 3, 5, 6, 7, 2, 8, 5, 2, 2, 7, 1, 2, 9, 7, 1, 5, 9, 8, 0, 9, 8, 9, 8, 6, 6, 5, 4, 1, 4, 0, 5, 7, 4, 4, 1, 0, 5, 0, 1, 1, 7, 6, 1, 8, 9, 7, 6, 3, 1, 4, 1, 7, 2, 3, 4, 7, 6, 4, 5, 3, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The limiting fractal dimension of a pattern generated by cellular automaton rule 150 is 1+log_2(phi).

This number is also involved in the evaluation of asymptotics for the number of odd terms in Pascal's trinomial triangle.

Also, the solution to 1 + 2^x = 4^x. See A328900 for solution to 2^x + 3^x = 4^x. - M. F. Hasler, Oct 30 2019

LINKS

Table of n, a(n) for n=0..99.

Steven Finch, Pascal Sebah and Zai-Qiao Bai, Odd Entries in Pascal's Trinomial Triangle, arXiv:0802.2654 [math.NT], 2008, page 5.

Daniel Glasscock, Joel Moreira, and Florian K. Richter, Additive transversality of fractal sets in the reals and the integers, arXiv:2007.05480 [math.NT], 2020. See p. 33.

Stephen Wolfram, Statistical mechanics of cellular automata, page 616.

FORMULA

log((1 + sqrt(5))/2)/log(2).

log(sqrt(5) + 1)/log(2) - 1. - M. F. Hasler, Oct 30 2019

EXAMPLE

0.6942419136306173017387902668985952234635672852271297159809898665414...

MATHEMATICA

RealDigits[Log[2, GoldenRatio], 10, 100] // First

PROG

(PARI) print(c=log(sqrt(5)+1)/log(2)-1); digits(c\.1^default(realprecision))[^-1] \\ [^-1] to discard possibly incorrect last digit. Use e.g. \p999 to get more digits. - M. F. Hasler, Oct 30 2019

CROSSREFS

Cf. A001622, A328912 (continued fraction).

Sequence in context: A341641 A215483 A153872 * A155784 A143735 A216117

Adjacent sequences:  A242205 A242206 A242207 * A242209 A242210 A242211

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, May 07 2014

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 03:23 EST 2021. Contains 349625 sequences. (Running on oeis4.)