login
Number of low discrepancy sequences in base 5.
(Formerly M0478)
3

%I M0478 #31 Sep 13 2023 09:43:20

%S 0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,12,14,16,18,20,22,24,26,28,30,32,34,

%T 36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,

%U 82,84,86,88,90,93,96,99,102,105,108,111,114,117,120,123,126,129,132,135,138,141,144,147,150,153,156,159,162

%N Number of low discrepancy sequences in base 5.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harald Niederreiter, <a href="http://dx.doi.org/10.1016/0022-314X(88)90025-X">Low-discrepancy and low-dispersion sequences</a>, J. Number Theory 30 (1988), no. 1, 51-70.

%t Np[b_, n_] := Np[b, n] = Sum[b^d*MoebiusMu[n/d], {d, Divisors[n]}]/n;

%t M[b_, n_] := If[n == 0, 0, Sum[Np[b, h], {h, 1, n}]];

%t nMax[b_, s_] := Module[{n}, For[n = 0, True, n++, If[M[b, n] > s, Return[n - 1]]]];

%t a[s_] := Module[{n, b}, b = 5; n = nMax[b, s]; n*(s - M[b, n]) + Sum[(h - 1)*Np[b, h], {h, 1, n}]];

%t Table[a[n], {n, 1, 79}] (* _Jean-François Alcover_, Sep 12 2023, after _R. J. Mathar_ in A005356 *)

%Y Cf. A005356 (base 2), A005357 (base 3), A005377 (base 4).

%K nonn

%O 1,7

%A _N. J. A. Sloane_, _Simon Plouffe_

%E More terms from _Sean A. Irvine_, May 27 2016