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A242208 Decimal expansion of log_2(phi), the logarithm to base 2 of phi, the "golden ratio" (1+sqrt(5))/2. 4
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.

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, page 5.

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

FORMULA

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

EXAMPLE

0.69424191363061730173879...

MATHEMATICA

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

CROSSREFS

Cf. A001622.

Sequence in context: A225053 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

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Last modified April 26 17:21 EDT 2017. Contains 285449 sequences.