A062964 Pi in hexadecimal.

3, 2, 4, 3, 15, 6, 10, 8, 8, 8, 5, 10, 3, 0, 8, 13, 3, 1, 3, 1, 9, 8, 10, 2, 14, 0, 3, 7, 0, 7, 3, 4, 4, 10, 4, 0, 9, 3, 8, 2, 2, 2, 9, 9, 15, 3, 1, 13, 0, 0, 8, 2, 14, 15, 10, 9, 8, 14, 12, 4, 14, 6, 12, 8, 9, 4, 5, 2, 8, 2, 1, 14, 6, 3, 8, 13, 0, 1, 3, 7, 7, 11, 14, 5, 4, 6, 6, 12, 15, 3, 4, 14, 9

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. 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, cf. 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

a(n) = 8*A004601(4n)+4*A004601(4n+1)+2*A004601(4n+2)+1*A004601(4n+3).

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

Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), A004604 (b=5), A004605 (b=6), A004606 (b=7), A006941 (b=8), A004608 (b=9), A000796 (b=10), A068436 (b=11), A068437 (b=12), A068438 (b=13), A068439 (b=14), A068440 (b=15), this sequence (b=16), A060707 (b=60).

Cf. A007514.

Sequence in context: A294209 A066257 A085591 * A010270 A230499 A023630

Adjacent sequences: A062961 A062962 A062963 * A062965 A062966 A062967

Keyword

easy,nonn,base,cons

Author

Robert Lozyniak (11(AT)onna.com), Jul 22 2001

Extensions

More terms from Henry Bottomley, Jul 24 2001

Status

approved