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 A213594 #13 Jan 12 2025 11:05:53 %S A213594 1,2,1,3,1,3,5,4,4,4,7,5,6,7,5,7,8,7,9,8,11,11,8,7,9,11,8,13,12,11,12, %T A213594 11,12,12,14,13,15,15,11,13,14,18,15,15,15,14,17,14,17,18,18,20,17,19, %U A213594 19,19,18,19,21,19,19,21,20,22,18,21,24,22,26,24,20 %N A213594 Greatest number k such that A048784(n) / 2^k is an integer. %C A213594 2-adic valuation of A048784. %C A213594 Property: a(n) > 0, that is A048784(n) is even, for n > 0. %H A213594 Charles R Greathouse IV, <a href="/A213594/b213594.txt">Table of n, a(n) for n = 1..10000</a> %e A213594 a(7) = 5 because A048784(7) / 2^5 = 32 / 32 = 1 is an integer. %p A213594 with(numtheory): for n from 1 to 100 do:ii:=0:for k from 500 by -1 to 1 while(ii=0) do: x:=evalf(tau(binomial(2*n,n))/2^k):if x=floor(x) then ii:=1: printf(`%d, `,k):else fi:od:od: %o A213594 (PARI) a(n)=valuation(numdiv(binomial(2*n,n)),2) \\ _Charles R Greathouse IV_, Jun 15 2012 %Y A213594 Cf. A000005, A048784. %K A213594 nonn %O A213594 1,2 %A A213594 _Michel Lagneau_, Jun 15 2012