login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the Zeckendorf representation of k also appear in that of n.
3

%I #13 Mar 27 2023 03:42:47

%S 0,0,1,0,2,0,3,0,1,3,4,0,5,0,1,5,6,0,2,5,7,0,8,0,1,8,9,0,2,8,10,0,3,8,

%T 11,0,1,3,4,8,9,11,12,0,13,0,1,13,14,0,2,13,15,0,3,13,16,0,1,3,4,13,

%U 14,16,17,0,5,13,18,0,1,5,6,13,14,18,19,0,2,5,7,13,15,18,20

%N Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the Zeckendorf representation of k also appear in that of n.

%C In other words, the n-th row lists the numbers k such that A003714(n) AND A003714(k) = A003714(k) (where AND denotes the bitwise AND operator).

%C The Zeckendorf representation is also known as the greedy Fibonacci representation (see A356771 for further details).

%H Rémy Sigrist, <a href="/A361755/b361755.txt">Table of n, a(n) for n = 0..10924</a> (rows for n = 0..610 flattened)

%H Rémy Sigrist, <a href="/A361755/a361755.gp.txt">PARI program</a>

%H <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>

%F T(n, 1) = 0.

%F T(n, 2) = A139764(n) for any n > 0.

%F T(n, 2^A007895(n)) = n.

%e Triangle T(n, k) begins:

%e n n-th row

%e -- ------------------------

%e 0 0

%e 1 0, 1

%e 2 0, 2

%e 3 0, 3

%e 4 0, 1, 3, 4

%e 5 0, 5

%e 6 0, 1, 5, 6

%e 7 0, 2, 5, 7

%e 8 0, 8

%e 9 0, 1, 8, 9

%e 10 0, 2, 8, 10

%e 11 0, 3, 8, 11

%e 12 0, 1, 3, 4, 8, 9, 11, 12

%o (PARI) See Links section.

%Y See A361756 for a similar sequence.

%Y Cf. A003714, A007895, A139764, A295989, A356771.

%K nonn,tabf,base

%O 0,5

%A _Rémy Sigrist_, Mar 23 2023