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A062964
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Pi in hexadecimal.
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43
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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
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 17-28.
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LINKS
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FORMULA
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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
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EXAMPLE
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3.243f6a8885a308d3...
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MATHEMATICA
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RealDigits[ N[ Pi, 115], 16] [[1]]
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PROG
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(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
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CROSSREFS
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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).
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KEYWORD
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AUTHOR
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Robert Lozyniak (11(AT)onna.com), Jul 22 2001
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EXTENSIONS
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STATUS
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approved
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