login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102243 Expansion of Pi in golden base (i.e., in irrational base phi=(1+sqrt(5))/2). 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

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. 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, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 9 14:38 EST 2016. Contains 278971 sequences.