cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A102215 #28 Aug 07 2020 12:11:59
%S A102215 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,
%T A102215 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,
%U A102215 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
%N A102215 Expansion of Pi^2/50 in golden base (i.e., in irrational base phi = (1 + sqrt(5))/2).
%H A102215 D. H. Bailey, <a href="https://www.davidhbailey.com/dhbpapers/bbp-formulas.pdf">A compendium of BBP-type formulas for mathematical constants</a>.
%H A102215 J. Borwein and M. Chamberland, <a href="https://archive.siam.org/journals/categories/06-003.php">A golden example</a>.
%e A102215 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...
%t A102215 Join[{0,0,0},RealDigits[Pi^2/50,GoldenRatio,120][[1]]] (* _Harvey P. Dale_, Nov 06 2011 *)
%o A102215 (PARI)
%o A102215 default(realprecision,1000);
%o A102215 default(format,"g.28");
%o A102215 b=1.0/( (1+sqrt(5))/2 ); /* inverse base */
%o A102215 d=1.0; /* value of digit */
%o A102215 C=Pi^2/50;  /* Number to be converted */
%o A102215 { for (n=1, 1000,
%o A102215     d *= b; /* value of digit == b^n */
%o A102215     if ( d<=C,
%o A102215         C-=d;
%o A102215         print1("1, ");
%o A102215     , /* else */
%o A102215         print1("0, ");
%o A102215     );
%o A102215 );}
%o A102215 C /* check remaining value (should be well within precision) */
%o A102215 /* _Joerg Arndt_, Jan 24 2011 */
%K A102215 base,cons,nonn
%O A102215 1,1
%A A102215 _Benoit Cloitre_, Feb 18 2005