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 A307433 #90 Jul 19 2019 08:48:33 %S A307433 1,1,1,1,2,1,1,1,1,1,1,2,2,2,1,1,1,4,4,1,1,1,2,1,8,1,2,1,1,1,1,1,1,1, %T A307433 1,1,1,2,2,2,2,2,2,2,1,1,1,4,4,4,4,4,4,1,1,1,2,1,8,8,8,8,8,1,2,1,1,1, %U A307433 1,1,16,16,16,16,1,1,1,1,1,2,2,2,1,32,32,32,1,2,2,2,1 %N A307433 A special version of Pascal's triangle where only powers of 2 are permitted. %C A307433 If the sum of the two numbers above in the triangular array is not a power of 2 (A000079), then a 1 is put in its place. %C A307433 The ones in the table form a Sierpinski gasket (A047999). %C A307433 Apparently, for any k > 0, the value 2^k first occurs on row A206332(k). %C A307433 From _Bernard Schott_, May 05 2019: (Start) %C A307433 For any m, at row 2^m - 1, there is only a string of 2^m times the number 1, then at row 2^(m+1) - 2, comes out for the first time and only once, the power of 2 equals to 2^(2^m-1). At row 2^(m+1) - 1, there are again 2^(m+1) times the number 1. This cycle can go on. Under, a part of this triangle between row 2^3 -1 and 2^4 - 2 that visualizes the explanations. %C A307433 1 1 1 1 1 1 1 1 %C A307433 2 2 2 2 2 2 2 %C A307433 4 4 4 4 4 4 %C A307433 8 8 8 8 8 %C A307433 16 16 16 16 %C A307433 32 32 32 %C A307433 64 64 %C A307433 128 %C A307433 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (End) %H A307433 Rémy Sigrist, <a href="/A307433/b307433.txt">Table of n, a(n) for n = 0..8255</a> (rows n = 0..127) %H A307433 Rémy Sigrist, <a href="/A307433/a307433.png">Colored representation of the first 1024 rows</a> (where the hue is function of log(T(n,k))) %H A307433 Rémy Sigrist, <a href="/A307433/a307433_1.png">Colored representation of the first 1024 rows</a> (where black pixels correspond to ones) %e A307433 The triangle begins: %e A307433 1 %e A307433 1 1 %e A307433 1 2 1 %e A307433 1 1 1 1 %e A307433 1 2 2 2 1 %e A307433 1 1 4 4 1 1 %e A307433 1 2 1 8 1 2 1 %e A307433 1 1 1 1 1 1 1 1 %e A307433 1 2 2 2 2 2 2 2 1 %e A307433 1 1 4 4 4 4 4 4 1 1 %e A307433 1 2 1 8 8 8 8 8 1 2 1 %e A307433 1 1 1 1 16 16 16 16 1 1 1 1 %e A307433 1 2 2 2 1 32 32 32 1 2 2 2 1 %e A307433 1 1 4 4 1 1 64 64 1 1 4 4 1 1 %e A307433 1 2 1 8 1 2 1 128 1 2 1 8 1 2 1 %e A307433 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 %o A307433 (PARI) for (r=1, 13, apply(v -> print1 (v", "), row=vector(r, k, if (k==1 || k==r, 1, hammingweight(s=row[k-1]+row[k])==1, s, 1)))) %Y A307433 Cf. A000079, A007318, A047999, A206332, A307116 (analog with Fibonacci numbers). %K A307433 nonn,tabl,look %O A307433 0,5 %A A307433 _Rémy Sigrist_, May 05 2019