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A102243 Expansion of Pi in golden base (i.e., in irrational base phi = (1+sqrt(5))/2) = A001622. 6
1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

3

COMMENTS

George Bergman wrote his paper when he was 12. Mike Wallace interviewed him when Bergman was 14. - Robert G. Wilson v, Mar 14 2014

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 3..1002 (offset adapted by Georg Fischer, Jan 24 2019)

George Bergman, A number system with an irrational base, Math. Mag. 31 (1957), pp. 98-110.

Mike Wallace, Mike Wallace Asks George Bergman: What Makes a Genius Tick?, Math. Mag. 31 (1958), p. 282.

EXAMPLE

Pi = phi^2 + 1/phi^2 + 1/phi^5 + 1/phi^7 + ... thus Pi = 100.0100101010010001010101000001010... in golden base.

MATHEMATICA

RealDigits[Pi, GoldenRatio, 111][[1]] (* Robert G. Wilson v, Feb 26 2010 *)

PROG

(PARI) f=(1+sqrt(5))/2; z=Pi; b=0; m=100; for(n=1, m, c=ceil(log(z)/log(1/f)); z=z-1/f^c; b=b+1./10^c; if(n==m, print1(b, ", ")))

CROSSREFS

Cf. A000796, A001622, A004601, A004602, A004603, A004604, A004605, A004606, A004608, A006941, A062964, A068436, A068437, A068438, A068439, A068440, A238897.

Sequence in context: A121262 A181923 A290098 * A173859 A202108 A287530

Adjacent sequences:  A102240 A102241 A102242 * A102244 A102245 A102246

KEYWORD

cons,base,nonn

AUTHOR

Benoit Cloitre, Feb 18 2005

EXTENSIONS

Offset corrected by Lee A. Newberg, Apr 13 2018

STATUS

approved

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Last modified April 9 20:55 EDT 2020. Contains 333363 sequences. (Running on oeis4.)