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A138253 Beatty discrepancy of the complementary equation b(n)=a(a(n))+n. 4
1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Suppose that (a(n)) and (b(n)) are complementary sequences that satisfy a complementary equation b(n)=f(a(n),n) and that the limits r = lim(a(n)/n) and s = lim(b(n)/n) exist and are both in the open interval (0,1).  Let c(n)=floor(a(n)) and d(n)=floor(b(n)), so that (c(n)) and d(n)) are a pair of Beatty sequences.  Define e(n) = d(n)-f(c(n),n).  The sequence (e(n)) is here introduced as the Beatty discrepancy of the complementary equation b(n)=f(a(n),n).  In the case at hand, (e(n)) measures the closeness of the pair (A136495,A136496) to the Beatty pair (A138251,A138252).

LINKS

Table of n, a(n) for n=1..105.

FORMULA

A138253(n) = d(n)-c(c(n))-n, where c(n)=A138251(n), d(n)=A138252(n).

EXAMPLE

d(1)-c(c(1))-1=3-1-1=1;

d(2)-c(c(2))-2=6-2-2=2;

d(3)-c(c(3))-3=9-5-3=1;

d(4)-c(c(4))-4=12-7-4=1.

CROSSREFS

Cf. A136495, A136496, A138251, A138252.

Sequence in context: A274372 A037800 A144411 * A261447 A287325 A286133

Adjacent sequences:  A138250 A138251 A138252 * A138254 A138255 A138256

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 09 2008

STATUS

approved

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Last modified August 17 18:38 EDT 2017. Contains 290655 sequences.