A349102 -id:A349102 - cp's OEIS frontend

A352583 a(n) is the value of the cell in the Wythoff array that lies in the next row and same column as the cell containing n.

4, 7, 11, 6, 18, 9, 10, 29, 12, 15, 16, 14, 47, 17, 20, 24, 19, 26, 22, 23, 76, 25, 28, 32, 27, 39, 30, 31, 42, 33, 36, 37, 35, 123, 38, 41, 45, 40, 52, 43, 44, 63, 46, 49, 50, 48, 68, 51, 54, 58, 53, 60, 56, 57, 199, 59, 62, 66, 61, 73, 64, 65, 84, 67, 70, 71, 69, 102, 72, 75

Offset: 1

Michel Marcus, Mar 21 2022

From Kevin Ryde, Jun 05 2022: (Start)
a(n) is n with the "odd" part (A348853) of its Zeckendorf representation increased to the next greater "odd" number.
This increase is Zeckendorf digits +10 or +100 at the odd part, according to whether the final digits there are ..101 or ..001, respectively.
A354321(n) is the first of those three digits so that a(n) = n + Fibonacci(A035612(n) + 3 - A354321(n)).
(End)

			The Wythoff array (A035513 or A083412) begins:
   1    2    3    5    8 ...
   4    7   11   18   29 ...
   6   10   16   26   42 ...
   ...
so a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 6, ...

Cf. A035513 and A083412 (Wythoff array), A003603 (row number), A035612 (column number).
Cf. A348853 (odd part), A354321 (above 01), A000045 (Fibonacci numbers).
Cf. A022342 (same row, next column).
Cf. A349102 (binary increase odd).

T(n,k) = (n+sqrtint(5*n^2))\2*fibonacci(k+1) + (n-1)*fibonacci(k); \\ A035513
cell(n) = for (r=1, oo, for (c=1, oo, if (T(r,c) == n, return([r, c])); if (T(r,c) > n, break););); \\ see A003603 and A035612
a(n) = {my(pos = cell(n)); T(pos[1]+1, pos[2]);}

{ my(phi=quadgen(5),s=phi-1,c=2*phi-3);
a(n) = my(t=n,k=3,r);
  until(r

cp's OEIS Frontend

A352583 a(n) is the value of the cell in the Wythoff array that lies in the next row and same column as the cell containing n.

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