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 A227833 #16 Jul 09 2025 04:37:21 %S A227833 0,0,0,0,1,1,0,0,0,0,1,2,3,5,5,3,2,1,0,0,0,0,1,1,0,0,0,0,1,2,3,5,6,6, %T A227833 7,8,9,11,13,15,18,18,15,13,11,9,8,7,6,6,5,3,2,1,0,0,0,0,1,1,0,0,0,0, %U A227833 1,2,3,5,5,3,2,1,0,0,0,0,1,1,0,0,0,0,1,2,3,5,6,6,7,8,9,11,13,15,18,19,18,18,18,18,19 %N A227833 3-adic valuation of A005130(n). %C A227833 3^a(n) is the highest power of 3 dividing A005130(n). %H A227833 Amiram Eldar, <a href="/A227833/b227833.txt">Table of n, a(n) for n = 0..10000</a> %F A227833 From _Amiram Eldar_, Feb 21 2021: (Start) %F A227833 a(n) = A007949(A005130(n)). %F A227833 a(n) = a(n-1) + (s(2*n-2) + s(2*n-1) - s(n-1) - s(3*n-2))/2, where s(n) = A053735(n). (End) %t A227833 s[n_] := Plus @@ IntegerDigits[n, 3]; a[0] = 0; a[n_] := a[n] = a[n - 1] + (s[2*n - 2] + s[2*n - 1] - s[n - 1] - s[3*n - 2])/2; Array[a, 101, 0] (* _Amiram Eldar_, Feb 21 2021 *) %o A227833 (Magma) A005130:=func<i | IsZero(i) select 1 else &*[Factorial(3*k+1)/Factorial(i+k): k in [0..i-1]]>; [Valuation(A005130(n),3): n in [0..100]]; // _Bruno Berselli_, Aug 05 2013 %Y A227833 Cf. A005130, A007949, A053735, A194827. %K A227833 nonn %O A227833 0,12 %A A227833 _N. J. A. Sloane_, Aug 04 2013, based on a suggestion from Victor H. Moll