A140099 - OEIS

%I #30 Sep 13 2016 21:42:44

%S 2,5,8,11,14,17,19,22,25,28,31,34,36,39,42,45,48,51,53,56,59,62,65,68,

%T 70,73,76,79,82,85,88,90,93,96,99,102,105,107,110,113,116,119,122,124,

%U 127,130,133,136,139,141,144,147,150,153,156,159,161,164,167,170,173

%N A Beatty sequence: a(n) = [n*(1+t)], where t = tribonacci constant (A058265); complement of A140098.

%C Note that A276385 agrees with this sequence for n <= 17160 but disagrees beyond that point. In fact a(17161) = 48725, whereas A276385(17161) = 48724. - _N. J. A. Sloane_, Sep 03 2016

%C Also somewhat similar to but different from A109232. - _N. J. A. Sloane_, Sep 04 2016

%H Harvey P. Dale and N. J. A. Sloane, <a href="/A140099/b140099.txt">Table of n, a(n) for n = 1..20000</a>, Aug 29 2016 (First 1000 terms from Harvey P. Dale)

%H N. J. A. Sloane, <a href="/A140099/a140099.txt">Table of n, a(n) for n = 1..100000</a>

%F For n >= 1, a(n) = A158919(n)+n. - _N. J. A. Sloane_, Sep 04 2016

%e Tribonacci constant: t = 1.839286755214161132551852564653286600...

%t With[{tc=1/3 (1+Surd[19-3Sqrt[33],3])+1/3 Surd[19+3Sqrt[33],3]},Array[ Floor[ (1+tc)*#]&,70]] (* _Harvey P. Dale_, Dec 05 2013 *)

%o (PARI) {a(n)=local(t=(1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3))/3);floor(n*(1+t))}

%Y Cf. A140098 (complement), A140101, A058265, A109232, A276385.

%Y See also A158919 (Beatty sequence for tribonacci constant tau), A275926 (deviation from A140101).

%K nonn

%O 1,1

%A _Paul D. Hanna_, Jun 01 2008