This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A361755 #13 Mar 27 2023 03:42:47 %S A361755 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 A361755 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 A361755 14,16,17,0,5,13,18,0,1,5,6,13,14,18,19,0,2,5,7,13,15,18,20 %N A361755 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 A361755 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 A361755 The Zeckendorf representation is also known as the greedy Fibonacci representation (see A356771 for further details). %H A361755 Rémy Sigrist, <a href="/A361755/b361755.txt">Table of n, a(n) for n = 0..10924</a> (rows for n = 0..610 flattened) %H A361755 Rémy Sigrist, <a href="/A361755/a361755.gp.txt">PARI program</a> %H A361755 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a> %F A361755 T(n, 1) = 0. %F A361755 T(n, 2) = A139764(n) for any n > 0. %F A361755 T(n, 2^A007895(n)) = n. %e A361755 Triangle T(n, k) begins: %e A361755 n n-th row %e A361755 -- ------------------------ %e A361755 0 0 %e A361755 1 0, 1 %e A361755 2 0, 2 %e A361755 3 0, 3 %e A361755 4 0, 1, 3, 4 %e A361755 5 0, 5 %e A361755 6 0, 1, 5, 6 %e A361755 7 0, 2, 5, 7 %e A361755 8 0, 8 %e A361755 9 0, 1, 8, 9 %e A361755 10 0, 2, 8, 10 %e A361755 11 0, 3, 8, 11 %e A361755 12 0, 1, 3, 4, 8, 9, 11, 12 %o A361755 (PARI) See Links section. %Y A361755 See A361756 for a similar sequence. %Y A361755 Cf. A003714, A007895, A139764, A295989, A356771. %K A361755 nonn,tabf,base %O A361755 0,5 %A A361755 _Rémy Sigrist_, Mar 23 2023