login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A246355 Rectangular array:  T(n,k) is the position in the infinite Fibonacci word s = A003849 at which the block s(2)..s(n+1) occurs for the k-th time. 2
2, 5, 2, 7, 5, 2, 10, 7, 7, 2, 13, 10, 10, 7, 2, 15, 13, 15, 10, 7, 2, 18, 15, 20, 15, 10, 10, 2, 20, 18, 23, 20, 15, 15, 10, 2, 23, 20, 28, 23, 20, 23, 15, 10, 2, 26, 23, 31, 28, 23, 31, 23, 15, 10, 2, 28, 26, 36, 31, 28, 36, 31, 23, 15, 10, 2, 31, 28, 41 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Assuming that every row of T is infinite, each row contains the next row as a proper subsequence.  Row 1 of A246354 and row 1 of A246355 partition the positive integers.

LINKS

Table of n, a(n) for n=1..69.

FORMULA

First 2 rows:  A001950 (upper Wythoff numbers);

next 3 rows:  A035336 (Wythoff BA numbers);

next 5 rows:  A134861 (Wythoff BAA numbers);

next 8 rows:  (Wythoff BAAA numbers).

(The patterns continue; in particular the number of identical consecutive rows is always a Fibonacci number, as in A000045.)

EXAMPLE

The upper Wythoff sequence, A001950 gives the positions of 1 in A003849, which begins thus:  0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1.  For n = 1, the block s(2)..s(2) is simply 1, which occurs at positions 2,5,7,10,13,... as in row 1 of T.  For n = 5, the block s(2)..s(6) is 1,0,0,1,0 which occurs at positions 2,7,10,15,20,23, ...

The first 6 rows follow:

2 .. 5 .. 7 ... 10 .. 13 .. 15 .. 18 ...

2 .. 5 .. 7 ... 10 .. 13 .. 15 .. 18 ...

2 .. 7 .. 10 .. 15 .. 20 .. 23 .. 28 ...

2 .. 7 .. 10 .. 15 .. 20 .. 23 .. 28 ...

2 .. 7 .. 10 .. 15 .. 20 .. 23 .. 28 ...

2 .. 10 . 15 .. 23 .. 31 .. 36 .. 44 ...

MATHEMATICA

z = 1000; s = Flatten[Nest[{#, #[[1]]} &, {0, 1}, 12]]; Flatten[Position[s, 1]]; b[m_, n_] := b[m, n] = Take[s, {m, n}]; z1 = 500; z2 = 12; t[k_] := t[k] = Take[Select[Range[1, z1], b[#, # + k] == b[2, 2 + k] &], z2]; Column[Table[t[k], {k, 0, z2}]](* A246355, array *)

w[n_, k_] := t[n][[k + 1]]; Table[w[n - k, k], {n, 0, z2 - 1}, {k, n, 0, -1}] // Flatten (* A246355, sequence *)

CROSSREFS

Cf. A003849, A246354.

Sequence in context: A198570 A190290 A246341 * A016580 A309324 A220072

Adjacent sequences:  A246352 A246353 A246354 * A246356 A246357 A246358

KEYWORD

nonn,easy,tabl

AUTHOR

Clark Kimberling, Aug 24 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)