A334348 - OEIS

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A334348

The terms in the Zeckendorf representation of T(n, k) correspond to the terms in common in the Zeckendorf representations of n and of k; square array T(n, k) read by antidiagonals, n, k >= 0.

4

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 3, 3, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 5, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 5, 6, 5, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,13

COMMENTS

This array has connections with the bitwise AND operator (A004198).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..11475 (antidiagonals 0..150)

Rémy Sigrist, Colored representation of (x, y) for 0 <= x, y <= 1000 (where the hue is function of T(x, y))

Rémy Sigrist, PARI program for A334348

Wikipedia, Zeckendorf's theorem

Index entries for sequences related to Zeckendorf expansion of n

FORMULA

T(n, k) = A022290(A003714(n) AND A003714(k)) (where AND denotes the bitwise AND operator, A004198).

T(n, 0) = 0.

T(n, n) = n.

T(n, k) = T(k, n).

T(m, T(n, k)) = T(T(m, n), k).

EXAMPLE

Square array begins:

n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13

---+----------------------------------------------

0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1| 0 1 0 0 1 0 1 0 0 1 0 0 1 0

2| 0 0 2 0 0 0 0 2 0 0 2 0 0 0

3| 0 0 0 3 3 0 0 0 0 0 0 3 3 0

4| 0 1 0 3 4 0 1 0 0 1 0 3 4 0

5| 0 0 0 0 0 5 5 5 0 0 0 0 0 0

6| 0 1 0 0 1 5 6 5 0 1 0 0 1 0

7| 0 0 2 0 0 5 5 7 0 0 2 0 0 0

8| 0 0 0 0 0 0 0 0 8 8 8 8 8 0

9| 0 1 0 0 1 0 1 0 8 9 8 8 9 0

10| 0 0 2 0 0 0 0 2 8 8 10 8 8 0

11| 0 0 0 3 3 0 0 0 8 8 8 11 11 0

12| 0 1 0 3 4 0 1 0 8 9 8 11 12 0

13| 0 0 0 0 0 0 0 0 0 0 0 0 0 13

PROG

(PARI) See Links section.

CROSSREFS

Cf. A003714, A022290, A004198, A332022, A332565.

Sequence in context: A285720 A269175 A086076 * A316717 A328831 A085981

Adjacent sequences: A334345 A334346 A334347 * A334349 A334350 A334351

KEYWORD

nonn,tabl,look,base

AUTHOR

Rémy Sigrist, Apr 24 2020

STATUS

approved