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

Author

Benoit Cloitre, Feb 18 2005

Keywords

• base
• cons
• nonn

Examples

			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...
		

Links

• D. H. Bailey, A compendium of BBP-type formulas for mathematical constants.
• J. Borwein and M. Chamberland, A golden example.

Programs

Mathematica

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

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 */