A102215 Expansion of Pi^2/50 in golden base (i.e., in irrational base phi = (1 + sqrt(5))/2).

0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1

Offset

1,1

Links

Table of n, a(n) for n=1..109.

D. H. Bailey, A compendium of BBP-type formulas for mathematical constants.

J. Borwein and M. Chamberland, A golden example.

Example

Pi^2/50 = 1/phi^4 + 1/phi^7 + 1/phi^9 + 1/phi^12 + ... thus the phinary expansion of Pi^2/50 is 0.0001001010010...

Mathematica

Join[{0, 0, 0}, RealDigits[Pi^2/50, GoldenRatio, 120][[1]]] (* Harvey P. Dale, Nov 06 2011 *)

Prog

(PARI)
default(realprecision, 1000);
default(format, "g.28");
b=1.0/( (1+sqrt(5))/2 ); /* inverse base */
d=1.0; /* value of digit */
C=Pi^2/50;  /* Number to be converted */
{ for (n=1, 1000,
    d *= b; /* value of digit == b^n */
    if ( d<=C,
        C-=d;
        print1("1, ");
    , /* else */
        print1("0, ");
    );
); }
C /* check remaining value (should be well within precision) */
/* Joerg Arndt, Jan 24 2011 */

Crossrefs

Sequence in context: A100283 A320927 A134391 * A288508 A262588 A234577

Adjacent sequences: A102212 A102213 A102214 * A102216 A102217 A102218

Keyword

base,cons,nonn

Author

Benoit Cloitre, Feb 18 2005

Status

approved