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Search: a091649 -id:a091649
Displaying 1-3 of 3 results found. page 1
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A060707 Base-60 (Babylonian or sexagesimal) expansion of Pi. +10
25
3, 8, 29, 44, 0, 47, 25, 53, 7, 24, 57, 36, 17, 43, 4, 29, 7, 10, 3, 41, 17, 52, 36, 12, 14, 36, 44, 51, 50, 15, 33, 7, 23, 59, 9, 13, 48, 22, 12, 21, 45, 22, 56, 47, 39, 44, 28, 37, 58, 23, 21, 11, 56, 33, 22, 40, 42, 31, 6, 6, 3, 46, 16, 52, 2, 48, 33, 24, 38, 33, 22, 1, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
Mohammad K. Azarian, Al-Risala al-Muhitiyya: A Summary, Missouri Journal of Mathematical Sciences, Vol. 22, No. 2, 2010, pp. 64-85.
Mohammad K. Azarian, The Introduction of Al-Risala al-Muhitiyya: An English Translation, International Journal of Pure and Applied Mathematics, Vol. 57, No. 6, 2009, pp. 903-914.
Mohammad K. Azarian, Al-Kashi's Fundamental Theorem, International Journal of Pure and Applied Mathematics, Vol. 14, No. 4, 2004, pp. 499-509. Mathematical Reviews, MR2005b:01021 (01A30), February 2005, p. 919. Zentralblatt MATH, Zbl 1059.01005.
Mohammad K. Azarian, Meftah al-hesab: A Summary, MJMS, Vol. 12, No. 2, Spring 2000, pp. 75-95. Mathematical Reviews, MR 1 764 526. Zentralblatt MATH, Zbl 1036.01002.
Mohammad K. Azarian, A Summary of Mathematical Works of Ghiyath ud-din Jamshid Kashani, Journal of Recreational Mathematics, Vol. 29(1), pp. 32-42, 1998.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pi Digits
MATHEMATICA
RealDigits[ Pi, 60, 75][[1]]
PROG
(PARI) { default(realprecision, 17900); x=Pi; for (n=1, 10000, d=floor(x); x=(x-d)*60; write("b060707.txt", n, " ", d)); } \\ Harry J. Smith, Jul 09 2009
CROSSREFS
Cf. A000796, A091649, A159991.
Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), this sequence (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), A062964 (b=16), A060707 (b=60). - Jason Kimberley, Dec 06 2012
KEYWORD
base,cons,nonn
AUTHOR
Robert G. Wilson v, Feb 05 2001
STATUS
approved
A159991 Powers of 60: a(n) = 60^n. +10
25
1, 60, 3600, 216000, 12960000, 777600000, 46656000000, 2799360000000, 167961600000000, 10077696000000000, 604661760000000000, 36279705600000000000, 2176782336000000000000, 130606940160000000000000, 7836416409600000000000000, 470184984576000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..150
Wikipedia, Sexagesimal
Index entries for linear recurrences with constant coefficients, signature (60).
FORMULA
a(n) = A000400(n)*A011557(n) = A000351(n)*A001021(n) = A000302(n)*A001024(n) = A000244(n)*A009964(n). (Corrected by Robert B Fowler, Jan 25 2023)
From Muniru A Asiru, Nov 21 2018: (Start)
a(n) = 60^n.
a(n) = 60*a(n-1) for n > 0, a(0) = 1.
G.f.: 1/(1-60*x).
E.g.f: exp(60*x). (End)
a(n) = 1/a(-n) for all n in Z. - Michael Somos, Jan 01 2019
EXAMPLE
G.f. = 1 + 60*x + 3600*x^2 + 216000*x^3 + 12960000*x^4 + 77600000*x^5 + ... - Michael Somos, Jan 01 2019
MAPLE
[60^n$n=0..20]; # Muniru A Asiru, Nov 21 2018
MATHEMATICA
60^Range[0, 15] (* Harvey P. Dale, Jun 02 2011 *)
PROG
(Magma)[60^n: n in [0..20]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=60^n \\ Charles R Greathouse IV, May 02 2011
(Maxima) A159991(n):=60^n$
makelist(A159991(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(PARI) a(n)=60^n \\ Charles R Greathouse IV, Jun 19 2015
(PARI) powers(60, 8) \\ Charles R Greathouse IV, Jun 19 2015
(GAP) List([0..20], n->60^n); # Muniru A Asiru, Nov 21 2018
(Python) for n in range(0, 20): print(60**n, end=', ') # Stefano Spezia, Nov 21 2018
CROSSREFS
Subsequence of A051037.
Cf. A159990, A159993, A159995, A088157, A091649, A125628, A091720, A091721, A091722, A060707, A070197.
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 01 2009
STATUS
approved
A125628 Version of sexagesimal expansion of 2*Pi given by the Persian mathematician Al-Kashi in the 15th Century. +10
2
6, 16, 59, 28, 1, 34, 51, 46, 14, 50 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The last digit is rounded up from 49, 55 (cf. A091649). - Georg Fischer, Aug 04 2021
REFERENCES
Mohammad K. Azarian, Al-Risala al-Muhitiyya: A Summary, Missouri Journal of Mathematical Sciences, Vol. 22, No. 2, 2010, pp. 64-85.
Mohammad K. Azarian, The Introduction of Al-Risala al-Muhitiyya: An English Translation, International Journal of Pure and Applied Mathematics, Vol. 57, No. 6, 2009 , pp. 903-914.
Mohammad K. Azarian, Al-Kashi's Fundamental Theorem, International Journal of Pure and Applied Mathematics, Vol. 14, No. 4, 2004, pp. 499-509. Mathematical Reviews, MR2005b:01021 (01A30), February 2005, p. 919. Zentralblatt MATH, Zbl 1059.01005.
Mohammad K. Azarian, Meftah al-hesab: A Summary, MJMS, Vol. 12, No. 2, Spring 2000, pp. 75-95. Mathematical Reviews, MR 1 764 526. Zentralblatt MATH, Zbl 1036.01002.
Mohammad K. Azarian, A Summary of Mathematical Works of Ghiyath ud-din Jamshid Kashani, Journal of Recreational Mathematics, Vol. 29(1), pp. 32-42, 1998.
LINKS
Table of n, a(n) for n=1..10.
Wikipedia, Computation of 2 Pi
EXAMPLE
2*Pi ~= 6; 16, 59, 28, 1, 34, 51, 46, 14, 50.
CROSSREFS
Cf. A000796, A011545, A037000, A091649.
Cf. A159991. - Reinhard Zumkeller, May 02 2009
KEYWORD
nonn,base,fini,full
AUTHOR
Mohammad K. Azarian, Apr 08 2008
STATUS
approved
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Last modified September 5 17:16 EDT 2024. Contains 375700 sequences. (Running on oeis4.)