

A005357


Number of low discrepancy sequences in base 3.
(Formerly M0637)


3



0, 0, 0, 1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177
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OFFSET

1,5


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..58.
Harald Niederreiter, Lowdiscrepancy and lowdispersion sequences, J. Number Theory 30 (1988), no. 1, 5170.


FORMULA

Let N(b,n) = (1/n) * Sum_{dn} mobius(n/d) * b^d. Let M(b,n) = Sum_{k=1..n} N(b,k) with M(b,0) = 0. Let r = r(b,n) be the largest value r such that M(b,r) <= n. Then a(n) = Sum_{h=1..r} (h1) * N(3, h) + r * (n  M(3, r)) [From Niederreiter paper].  Sean A. Irvine, May 27 2016


CROSSREFS

Cf. A005356 (base 2), A005377 (base 4), A005358 (base 5).
Sequence in context: A336119 A213511 A092919 * A324697 A082664 A342008
Adjacent sequences: A005354 A005355 A005356 * A005358 A005359 A005360


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Simon Plouffe


EXTENSIONS

a(33) onwards corrected and incorrect g.f. removed by Sean A. Irvine, May 27 2016


STATUS

approved



