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%I #37 Mar 29 2019 13:41:23
%S 2,4,6,8,10,13,15,17,19,21,24,26,28,30,32,35,37,39,41,43,46,48,50,52,
%T 54,56,59,61,63,65,67,70,72,74,76,78,81,83,85,87,89,92,94,96,98,100,
%U 102,105,107,109,111,113,116,118,120,122,124,127,129,131,133,135,138,140,142,144,146,149,151,153,155,157,159,162,164,166,168,170,173,175,177,179,181,184,186,188,190,192,195,197,199,201,203,205,208,210,212,214,216,219,221,223,225,227,230,232,234,236,238,241,243
%N Complement of A158919: complementary Beatty sequence to the Beatty sequence defined by the tribonacci constant tau = A058265.
%C This is the Beatty sequence for tau_prime = 2.191487883953118747061354268227517294...,
%C defined by 1/tau + 1/tau_prime = 1.
%C Differs from A172278 at n = 162, 209, 256, 303, 324, ...
%C Note that Beatty sequences do not normally include 0 - see the classic pair A000201, A001950. - _N. J. A. Sloane_, Oct 19 2018
%C Note that the tribonacci numbers T = A000073 related to the ternary sequence A080843 lead to the three complementary sequences for the nonnegative integers AT(n) = A278040(n), BT(n) = A278039(n) and CT(n) = A278041(n). - _Wolfdieter Lang_, Sep 08 2018
%H R. J. Mathar, <a href="/A276383/b276383.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Beatty_sequence">Beatty Sequence </a>
%F a(n) = floor(n*tau_prime), with tau_prime = tau/(tau - 1), where tau is the tribonacci constant A058265.
%F tau_prime = (1 + (19 + 3*sqrt(33))^(1/3) + (19 - 3*sqrt(33))^(1/3)) / (-2 + (19 + 3*sqrt(33))^(1/3) + (19 - 3*sqrt(33))^(1/3)). - _Wolfdieter Lang_, Sep 08 2018
%e Comments from _Wolfdieter Lang_, Sep 08 2018 (Start):
%e The complementary sequences A158919 and A276383 begin:
%e n: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
%e A158919: 1 3 5 7 9 11 12 14 16 18 20 22 23 25 27 29 31 33 34 36 ...
%e A276383: 2 4 6 8 10 13 15 17 19 21 24 26 28 30 32 35 37 39 41 43 ...
%e --------------------------------------------------------------------
%e The complementary sequences AT, BT and CT begin:
%e n: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
%e AT: 1 5 8 12 14 18 21 25 29 32 36 38 42 45 49 52 56 58 62 65 ...
%e BT: 0 2 4 6 7 9 11 13 15 17 19 20 22 24 26 28 30 31 33 35 ...
%e CT: 3 10 16 23 27 34 40 47 54 60 67 71 78 84 91 97 104 108 115 121 ...
%e (End)
%p A276383 := proc(n)
%p Tau := (1/3)*(1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3));
%p taupr := 1/(1-1/Tau) ;
%p floor(n*taupr) ;
%p end proc: # _R. J. Mathar_, Sep 04 2016
%p a:=proc(n) local s,t; t:=evalf(solve(x^3-x^2-x-1=0,x),120)[1]; s:=t/(t-1); floor(n*s) end; seq(a(n),n=0..70); # _Muniru A Asiru_, Oct 16 2018
%Y Cf. A000201, A001950, A058265, A158919.
%Y Cf. also A000073, A080843, A276383, A278039, A278040, A278041, A316711.
%Y Similar to but strictly different from A172278.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Sep 02 2016
%E Edited by _N. J. A. Sloane_, Oct 19 2018 at the suggestion of Georg Fischer