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 A334348 #15 Aug 03 2022 17:42:01 %S A334348 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, %T A334348 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, %U A334348 0,0,0,5,5,0,0,0,0,0,0,0,2,0,0,5,6,5,0 %N 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. %C A334348 This array has connections with the bitwise AND operator (A004198). %H A334348 Rémy Sigrist, <a href="/A334348/b334348.txt">Table of n, a(n) for n = 0..11475</a> (antidiagonals 0..150) %H A334348 Rémy Sigrist, <a href="/A334348/a334348.png">Colored representation of (x, y) for 0 <= x, y <= 1000</a> (where the hue is function of T(x, y)) %H A334348 Rémy Sigrist, <a href="/A334348/a334348.gp.txt">PARI program for A334348</a> %H A334348 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zeckendorf's_theorem">Zeckendorf's theorem</a> %H A334348 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a> %F A334348 T(n, k) = A022290(A003714(n) AND A003714(k)) (where AND denotes the bitwise AND operator, A004198). %F A334348 T(n, 0) = 0. %F A334348 T(n, n) = n. %F A334348 T(n, k) = T(k, n). %F A334348 T(m, T(n, k)) = T(T(m, n), k). %e A334348 Square array begins: %e A334348 n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 %e A334348 ---+---------------------------------------------- %e A334348 0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %e A334348 1| 0 1 0 0 1 0 1 0 0 1 0 0 1 0 %e A334348 2| 0 0 2 0 0 0 0 2 0 0 2 0 0 0 %e A334348 3| 0 0 0 3 3 0 0 0 0 0 0 3 3 0 %e A334348 4| 0 1 0 3 4 0 1 0 0 1 0 3 4 0 %e A334348 5| 0 0 0 0 0 5 5 5 0 0 0 0 0 0 %e A334348 6| 0 1 0 0 1 5 6 5 0 1 0 0 1 0 %e A334348 7| 0 0 2 0 0 5 5 7 0 0 2 0 0 0 %e A334348 8| 0 0 0 0 0 0 0 0 8 8 8 8 8 0 %e A334348 9| 0 1 0 0 1 0 1 0 8 9 8 8 9 0 %e A334348 10| 0 0 2 0 0 0 0 2 8 8 10 8 8 0 %e A334348 11| 0 0 0 3 3 0 0 0 8 8 8 11 11 0 %e A334348 12| 0 1 0 3 4 0 1 0 8 9 8 11 12 0 %e A334348 13| 0 0 0 0 0 0 0 0 0 0 0 0 0 13 %o A334348 (PARI) See Links section. %Y A334348 Cf. A003714, A022290, A004198, A332022, A332565. %K A334348 nonn,tabl,look,base %O A334348 0,13 %A A334348 _Rémy Sigrist_, Apr 24 2020