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A005356 Number of low discrepancy sequences in base 2.
(Formerly M2435)
4
0, 0, 1, 3, 5, 8, 11, 14, 18, 22, 26, 30, 34, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 198, 205, 212, 219, 226, 233, 240, 247, 254, 261, 268, 275, 282, 289, 296 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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..56.

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

MAPLE

N := proc(b, n)

    option remember;

    local d;

    add(b^d*numtheory[mobius](n/d), d=numtheory[divisors](n)) ;

    %/n ;

end proc:

M := proc(b, n)

    local h;

    if n = 0 then

        0;

    else

        add(N(b, h), h=1..n) ;

    end if;

end proc:

nMax := proc(b, s)

    local n;

    for n from 0 do

        if M(b, n) > s then

            return n-1 ;

        end if;

    end do:

end proc:

A005356 := proc(s)

    local n, b;

    b := 2 ;

    n := nMax(b, s) ;

    n*(s-M(b, n))+add( (h-1)*N(b, h), h=1..n) ;

end proc:

seq(A005356(n), n=1..40) ; # R. J. Mathar, Jun 09 2016

CROSSREFS

Cf. A005357 (base 3), A005377 (base 4), A005358 (base 5).

Sequence in context: A052488 A076372 A248611 * A060432 A156023 A261223

Adjacent sequences:  A005353 A005354 A005355 * A005357 A005358 A005359

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

More terms from Sean A. Irvine, May 27 2016

STATUS

approved

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Last modified February 19 10:24 EST 2019. Contains 320310 sequences. (Running on oeis4.)