A140099 A Beatty sequence: a(n) = [n*(1+t)], where t = tribonacci constant (A058265); complement of A140098.

2, 5, 8, 11, 14, 17, 19, 22, 25, 28, 31, 34, 36, 39, 42, 45, 48, 51, 53, 56, 59, 62, 65, 68, 70, 73, 76, 79, 82, 85, 88, 90, 93, 96, 99, 102, 105, 107, 110, 113, 116, 119, 122, 124, 127, 130, 133, 136, 139, 141, 144, 147, 150, 153, 156, 159, 161, 164, 167, 170, 173

Offset: 1

Author

Paul D. Hanna, Jun 01 2008

Keywords

• nonn

Comments

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

Also somewhat similar to but different from A109232. - N. J. A. Sloane, Sep 04 2016

Examples

			Tribonacci constant: t = 1.839286755214161132551852564653286600...
		

Links

• Harvey P. Dale and N. J. A. Sloane, Table of n, a(n) for n = 1..20000, Aug 29 2016 (First 1000 terms from Harvey P. Dale)
• N. J. A. Sloane, Table of n, a(n) for n = 1..100000

Crossrefs

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

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

Programs

Mathematica

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 *)

PARI

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

Formula

For n >= 1, a(n) = A158919(n)+n. - N. J. A. Sloane, Sep 04 2016