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A184478 Lower s-Wythoff sequence, where s(n) = 3n + 1.  Complement of A184479. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 20 14:50 EDT 2019. Contains 326152 sequences. (Running on oeis4.)