OFFSET
1,1
COMMENTS
Bailey and Crandall conjecture that the terms of this sequence, apart from the first, are given by the formula floor(16*(x(n) - floor(x(n)))), where x(n) is determined by the recurrence equation x(n) = 16*x(n-1) + (120*n^2 - 89*n + 16)/(512*n^4 - 1024*n^3 + 712*n^2 - 206*n + 21) with the initial condition x(0) = 0 (see A374334). They have numerically verified the conjecture for the first 100000 terms of the sequence. - Peter Bala, Oct 31 2013
Bailey, Borwein & Plouffe's ("BBP") formula allows one to compute the n-th hexadecimal digit of Pi without calculating the preceding digits (see Wikipedia link). - M. F. Hasler, Mar 14 2015
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 17-28.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..20000
D. H. Bailey, Compendium of BBP-Type Formulas for Mathematical Constants.
D. H. Bailey and R. E. Crandall, On the Random Character of Fundamental Constant Expansions, Experiment. Math. Volume 10, Issue 2 (2001), 175-190.
CalcCrypto, Pi in Hexadecimal. [Broken link]
S. R. Finch, The Miraculous Bailey-Borwein-Plouffe Pi Algorithm.
Steve Pagliarulo, Stu's pi page: base 16 (31 pages of numbers). [Dead link]
Johnny Vogler, More digits.
Wikipedia, Bailey-Borwein-Plouffe formula.
FORMULA
If Pi is the expansion of Pi in base 10, Pi=3.1415926...: a(n) = floor(16^n*Pi) - 16*floor(16^(n-1)*Pi). - Benoit Cloitre, Mar 09 2002
EXAMPLE
3.243f6a8885a308d3...
MATHEMATICA
RealDigits[ N[ Pi, 115], 16] [[1]]
PROG
(PARI) { default(realprecision, 24300); x=Pi; for (n=1, 20000, d=floor(x); x=(x-d)*16; write("b062964.txt", n, " ", d)); } \\ Harry J. Smith, Apr 27 2009
(PARI) N=50; default(realprecision, .75*N); A062964=digits(Pi*16^N\1, 16) \\ M. F. Hasler, Mar 14 2015
CROSSREFS
KEYWORD
AUTHOR
Robert Lozyniak (11(AT)onna.com), Jul 22 2001
EXTENSIONS
More terms from Henry Bottomley, Jul 24 2001
STATUS
approved