A281863 Alternating powers of 60 and 10 times powers of 60.

1, 10, 60, 600, 3600, 36000, 216000, 2160000, 12960000, 129600000, 777600000, 7776000000, 46656000000, 466560000000, 2799360000000, 27993600000000, 167961600000000, 1679616000000000, 10077696000000000, 100776960000000000, 604661760000000000

Offset: 0

Author

Wolfdieter Lang, Feb 19 2017

Keywords

• nonn
• easy

Comments

These numbers are the values for the positions in the Sumerian (and Babylonian) alternating sexagesimal - decimal system (used at least up to 10*60^2 = 36000, but here extended).

For the numbers in this mixed base system see A055643. For the number of symbols needed for representing n see A131650. For the number of digits (including 0) of the representation of n see A282622.

References

• Georges Ifrah, Histoire Universelle des Chiffres, Paris, 1981.
• Georges Ifrah, From one to zero, A universal history of numbers, Viking Penguin Inc., 1985.
• Georges Ifrah, Universalgeschichte der Zahlen, Campus Verlag, Frankfurt, New York, 2. Auflage, 1987, pp. 210-221.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 127.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,60).

Crossrefs

Cf. A131650, A055643, A282622.

Programs

Mathematica

LinearRecurrence[{0,60},{1,10},21] (* or *) a[0]=1;a[1]=10;a[n_]:=60*a[n-2];Table[a[n],{n,0,20}] (* Indranil Ghosh, Feb 21 2017 *)

PARI

Vec((1 + 10*x) / (1 - 60*x^2) + O(x^30)) \\ Colin Barker, Feb 21 2017

Formula

a(2*n) = 60^(n/2), a(2*n+1) = 10*60^((n-1)/2), n >= 0.

From Colin Barker, Feb 21 2017: (Start)

a(n) = 60*a(n-2) for n>1.

G.f.: (1 + 10*x) / (1 - 60*x^2). (End)

E.g.f.: cosh(2*sqrt(15)*x) + sqrt(5/3)*sinh(2*sqrt(15)*x). - Stefano Spezia, Sep 08 2024