A005358 Number of low discrepancy sequences in base 5. (Formerly M0478)

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

Offset

1,7

References

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

Links

Table of n, a(n) for n=1..79.

Harald Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), no. 1, 51-70.

Mathematica

Np[b_, n_] := Np[b, n] = Sum[b^d*MoebiusMu[n/d], {d, Divisors[n]}]/n;
M[b_, n_] := If[n == 0, 0, Sum[Np[b, h], {h, 1, n}]];
nMax[b_, s_] := Module[{n}, For[n = 0, True, n++, If[M[b, n] > s, Return[n - 1]]]];
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}]];
Table[a[n], {n, 1, 79}] (* Jean-François Alcover, Sep 12 2023, after R. J. Mathar in A005356 *)

Crossrefs

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

Sequence in context: A098952 A144688 A164836 * A032518 A131242 A008728

Adjacent sequences: A005355 A005356 A005357 * A005359 A005360 A005361

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from Sean A. Irvine, May 27 2016

Status

approved