

A102243


Expansion of Pi in golden base (i.e., in irrational base phi=(1+sqrt(5))/2).


5



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
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OFFSET

2,1


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 = 2..1001
George Bergman, A number system with an irrational base, Math. Mag. 31 (1957), pp. 98110.
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=z1/f^c; b=b+1./10^c; if(n==m, print1(b, ", ")))


CROSSREFS

Cf. A000796, A004601, A004602, A004603, A004604, A004605, A004606, A004608, A006941, A062964, A068436, A068437, A068438, A068439, A068440, A238897.
Sequence in context: A015777 A014017 A121262 * A173859 A202108 A104108
Adjacent sequences: A102240 A102241 A102242 * A102244 A102245 A102246


KEYWORD

base,cons,nonn


AUTHOR

Benoit Cloitre, Feb 18 2005


EXTENSIONS

Offset corrected by R. J. Mathar, Feb 05 2009


STATUS

approved



