Search: a091649 -id:a091649
|
|
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
|
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
|
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
|
|
|
AUTHOR
|
|
|
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
|
|
|
FORMULA
|
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)
|
|
EXAMPLE
|
G.f. = 1 + 60*x + 3600*x^2 + 216000*x^3 + 12960000*x^4 + 77600000*x^5 + ... - Michael Somos, Jan 01 2019
|
|
MAPLE
|
|
|
MATHEMATICA
|
|
|
PROG
|
(Python) for n in range(0, 20): print(60**n, end=', ') # Stefano Spezia, Nov 21 2018
|
|
CROSSREFS
|
Cf. A159990, A159993, A159995, A088157, A091649, A125628, A091720, A091721, A091722, A060707, A070197.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|
|
A125628
|
|
Version of sexagesimal expansion of 2*Pi given by the Persian mathematician Al-Kashi in the 15th Century.
|
|
+10
2
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
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
|
|
|
EXAMPLE
|
2*Pi ~= 6; 16, 59, 28, 1, 34, 51, 46, 14, 50.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,fini,full
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
Search completed in 0.005 seconds
|