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

1,2

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

Links

Table of n, a(n) for n=1..120.

Formula

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

Prog

(PARI) A184478_upto(N, s(n)=3*n+1, a=[1], U=a)={while(a[#a]<N, U=setunion(U, [a[#a], a[#a]+s(#a)]); while(#U>1&&U[2]==U[1]+1, U=U[^1]); a=concat(a, U[1]+1)); a} \\ M. F. Hasler, Jan 07 2019
(Magma) [(Floor(n*(-1+Sqrt(13))/2))+1: n in [0..120]]; // Vincenzo Librandi, Jan 08 2019

Crossrefs

Cf. A184117, A184479, A184480.

Sequence in context: A119931 A129989 A187572 * A188188 A230319 A319371

Adjacent sequences: A184475 A184476 A184477 * A184479 A184480 A184481

Keyword

nonn

Author

Clark Kimberling, Jan 15 2011

Status

approved