A281863 - OEIS

%I #33 Sep 08 2024 12:10:50

%S 1,10,60,600,3600,36000,216000,2160000,12960000,129600000,777600000,

%T 7776000000,46656000000,466560000000,2799360000000,27993600000000,

%U 167961600000000,1679616000000000,10077696000000000,100776960000000000,604661760000000000

%N Alternating powers of 60 and 10 times powers of 60.

%C 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).

%C 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.

%D Georges Ifrah, Histoire Universelle des Chiffres, Paris, 1981.

%D Georges Ifrah, From one to zero, A universal history of numbers, Viking Penguin Inc., 1985.

%D Georges Ifrah, Universalgeschichte der Zahlen, Campus  Verlag, Frankfurt, New York, 2. Auflage, 1987, pp. 210-221.

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 127.

%H Colin Barker, <a href="/A281863/b281863.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,60).

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

%F From _Colin Barker_, Feb 21 2017: (Start)

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

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

%F E.g.f.: cosh(2*sqrt(15)*x) + sqrt(5/3)*sinh(2*sqrt(15)*x). - _Stefano Spezia_, Sep 08 2024

%t 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 *)

%o (PARI) Vec((1 + 10*x) / (1 - 60*x^2) + O(x^30)) \\ _Colin Barker_, Feb 21 2017

%Y Cf. A131650, A055643, A282622.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Feb 19 2017