cp's OEIS Frontend

A075167 Number of edges in each rooted plane tree produced with the unranking algorithm presented in A075166, which is based on prime factorization.

%I A075167 #16 Jan 16 2015 10:18:52
%S A075167 0,1,2,2,3,3,4,3,3,4,5,4,6,5,4,3,7,4,8,5,5,6,9,4,4,7,4,6,10,5,11,4,6,
%T A075167 8,5,5,12,9,7,5,13,6,14,7,5,10,15,5,5,5,8,8,16,5,6,6,9,11,17,6,18,12,
%U A075167 6,4,7,7,19,9,10,6,20,5,21,13,5,10,6,8,22,6,4,14,23,7,8,15,11,7,24,6,7,11
%N A075167 Number of edges in each rooted plane tree produced with the unranking algorithm presented in A075166, which is based on prime factorization.
%C A075167 Each n occurs A000108(n) times in total.
%H A075167 Antti Karttunen, <a href="/A075167/b075167.txt">Table of n, a(n) for n = 1..10000</a>
%F A075167 a(n) = A106457(A106442(n)). - _Antti Karttunen_, May 09 2005
%F A075167 From _Antti Karttunen_, Jan 16 2015: (Start)
%F A075167 a(1) = 0; for n>1: a(n) = a(A071178(n)) + (A061395(n) - A061395(A051119(n))) + A253783(A051119(n)).
%F A075167 Other identities.
%F A075167 For all n >= 2, a(n) = A055642(A075166(n))/2. [Half of the number of decimal digits in A075166(n).]
%F A075167 For all n >= 2, a(n) = A029837(1+A075165(n))/2. [Half of the binary width of A075165(n).]
%F A075167 For all n >= 1, a(n) = A000120(A075165(n)). [Thus also the binary weight of A075165(n), because half of the bits are zeros.]
%F A075167 (End)
%o A075167 (Scheme, with memoization-macro definec)
%o A075167 (definec (A075167 n) (if (= 1 n) 0 (+ (A075167 (A071178 n)) (- (A061395 n) (A061395 (A051119 n))) (A253783 (A051119 n)))))
%o A075167 ;; _Antti Karttunen_, Jan 16 2015
%Y A075167 Permutation of A072643 and A106457.
%Y A075167 A253782 gives the positions where this sequence differs from A252464 (first time at n=16).
%Y A075167 Cf. A000108, A000120, A029837, A055642, A051119, A061395, A071178, A075165, A075166, A106442, A253783.
%Y A075167 Cf. also A106490.
%K A075167 nonn
%O A075167 1,3
%A A075167 _Antti Karttunen_, Sep 13 2002
%E A075167 More terms from _Antti Karttunen_, May 09 2005