A182656 Floor-sum sequence of r, with r=sqrt(3), and a(1)=1, a(2)=2.

1, 2, 5, 10, 12, 19, 20, 22, 24, 25, 29, 34, 36, 38, 39, 41, 43, 45, 46, 50, 51, 53, 55, 58, 60, 62, 64, 65, 67, 69, 71, 72, 74, 76, 77, 79, 81, 83, 84, 86, 88, 90, 91, 93, 95, 96, 98, 100, 102, 103, 105, 107, 109, 110, 112, 114, 116, 117

Offset

1,2

Comments

Let S be the set generated by these rules: (1) if m and n are in S and m<n, then floor(mr+nr) is in S; (2) two or more specific numbers are in S. The floor-sum sequence determined by (1) and (2) results by arranging the elements of S in strictly increasing order.

Let B be the Beatty sequence of r. Then a floor-sum sequence of r is a subsequence of B if and only if a(1) and a(2) are terms of B.

Links

Table of n, a(n) for n=1..58.

Example

a(3)=floor(r+2r)=5.

Crossrefs

Cf. A182653, A182654, A182655, A022838.

Sequence in context: A245480 A080792 A351062 * A090050 A274454 A192539

Adjacent sequences: A182653 A182654 A182655 * A182657 A182658 A182659

Keyword

nonn

Author

Clark Kimberling, Nov 26 2010

Status

approved