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A138330 Beatty discrepancy (defined in A138253) giving the closeness of the pair (A136497,A136498) to the Beatty pair (A001951,A001952). 1
1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Old definition was "Beatty discrepancy of the complementary equation b(n) = a(a(n)) + a(n)".

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..1000

Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

FORMULA

A138330(n) = d(n) - c(c(n)) - c(n), where c(n) = A001951 and d(n) = A001952.

A138330(n) = 2*n - A007069(n). - Benoit Cloitre, May 08 2008

A138330(n) = A059648(n+1) + 1. - Michel Dekking, Nov 11 2018

EXAMPLE

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

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

d(3) - c(c(3)) - c(3) = 10 - 5 - 4 = 1;

d(4) - c(c(4)) - c(4) = 13 - 7 - 5 = 1.

MAPLE

a:=n->2*n-floor(sqrt(2)*floor(sqrt(2)*n)): seq(a(n), n=1..120); # Muniru A Asiru, Nov 11 2018

MATHEMATICA

Table[2 n - Floor[Sqrt[2] Floor[Sqrt[2] n]], {n, 1, 100}] (* Vincenzo Librandi, Nov 12 2018 *)

PROG

(PARI) a(n)=2*n-floor(sqrt(2)*floor(sqrt(2)*n)) \\ Benoit Cloitre, May 08 2008

(MAGMA) [2*n - Floor(Sqrt(2)*Floor(Sqrt(2)*n)): n in [1..100]]; // Vincenzo Librandi, Nov 12 2018

CROSSREFS

Cf. A001951, A001952, A136497, A136498, A138253, A059648.

Sequence in context: A115722 A115721 A279497 * A128591 A254444 A102005

Adjacent sequences:  A138327 A138328 A138329 * A138331 A138332 A138333

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 14 2008

EXTENSIONS

Definition revised by N. J. A. Sloane, Dec 16 2018

STATUS

approved

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Last modified January 16 09:52 EST 2019. Contains 319188 sequences. (Running on oeis4.)