A184478 Lower s-Wythoff sequence, where s(n) = 3n + 1. Complement of A184479.

1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 90, 92, 93, 94, 96, 97, 98, 100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 117, 118, 119, 120, 122, 123, 124, 126, 127, 128, 130, 131, 132, 133, 135, 136, 137, 139, 140, 141, 143, 144, 145, 146, 148, 149, 150, 152, 153, 154, 156

Offset: 1

Author

Clark Kimberling, Jan 15 2011

Keywords

• nonn

Comments

See A184117 for the definition of lower and upper s-Wythoff sequences.

The sequence is defined by a(1) = 1 and for n > 1, a(n) is the smallest positive integer not in {a(k), a(k) + s(k); k < n}. - M. F. Hasler, Jan 07 2019

Crossrefs

Cf. A184117, A184479, A184480.

Programs

Magma

[(Floor(n*(-1+Sqrt(13))/2))+1: n in [0..120]]; // Vincenzo Librandi, Jan 08 2019

Maple

a:=n->floor(n*(-1+sqrt(13))/2+1): seq(a(n),n=0..120); # Muniru A Asiru, Jan 08 2019

Mathematica

k=3; r=-1; d=Sqrt[4+k^2];
a[n_]:=Floor[(1/2)(d+2-k)(n+r/(d+2))];
b[n_]:=Floor[(1/2)(d+2+k)(n-r/(d+2))];
Table[a[n],{n,120}]
Table[b[n],{n,120}]
Table[(Floor[n (-1 + Sqrt[13]) / 2]) + 1, {n, 0, 120}] (* Vincenzo Librandi, Jan 08 2019 *)

PARI

A184478_upto(N, s(n)=3*n+1, a=[1], U=a)={while(a[#a]1&&U[2]==U[1]+1, U=U[^1]); a=concat(a, U[1]+1)); a} \\ M. F. Hasler, Jan 07 2019

Formula

a(n) = A184479(n) - s(n). - M. F. Hasler, Jan 07 2019