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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A131650, A055643, A282622.

Sequence in context: A002493 A054364 A004309 * A219368 A052664 A090373

Adjacent sequences: A281860 A281861 A281862 * A281864 A281865 A281866

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 19 2017

Status

approved