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A062964 Pi in hexadecimal. 42
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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]
Steve Pagliarulo, Stu's pi page: base 16 (31 pages of numbers) [Dead link]
Johnny Vogler, More digits
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
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

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Last modified March 1 22:18 EST 2024. Contains 370443 sequences. (Running on oeis4.)