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 A130703 #11 Mar 31 2012 14:42:50 %S A130703 0,0,0,0,9,14,10,27,35,22,18,65,77,18,26,119,27,38,34,27,209,46,28,55, %T A130703 299,36,35,377,45,62,58,45,527,40,54,629,95,54,74,779,63,86,82,63,989, %U A130703 94,54,161,235,68,91,265,81,65,106,81,145,118,90,1769,1829 %N A130703 a(n) = smallest k such that A000217(n+1) = A000217(n) + (A000217(n) mod k), or 0 if no such k exists. %C A130703 a(n) is the weight of triangular numbers. %C A130703 The decomposition of triangular numbers into weight * level + gap is A000217(n) = a(n) * A184219(n) + (n + 1) if a(n) > 0. %H A130703 Remi Eismann, <a href="/A130703/b130703.txt">Table of n, a(n) for n=1..9999</a> %e A130703 For n = 1 we have A000217(n) = 1, A000217(n+1) = 3; there is no k such that 3 - 1 = 2 = (1 mod k), hence a(1) = 0. %e A130703 For n = 5 we have A000217(n) = 15, A000217(n+1) = 21; 9 is the smallest k such that 21 - 15 = 6 = (15 mod k), hence a(5) = 9. %e A130703 For n = 22 we have A000217(n) = 253, A000217(n+1) = 276; 46 is the smallest k such that 276 - 253 = 23 = (253 mod k), hence a(22) = 46. %Y A130703 Cf. A020639, A117078, A117563, A001223, A118534, A090369, A090368. %K A130703 nonn %O A130703 1,5 %A A130703 _Rémi Eismann_, Aug 16 2007 - Jan 10 2011