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A209637 Matula-numbers computed for rooted trees encoded by A071162 when interpreted in once-halved bit-tuple format.

%I A209637 #10 May 26 2017 08:55:08
%S A209637 1,2,3,4,5,7,6,8,11,17,13,19,10,14,12,16,31,59,41,67,29,43,37,53,22,
%T A209637 34,26,38,20,28,24,32,127,277,179,331,109,191,157,241,79,139,101,163,
%U A209637 71,107,89,131,62,118,82,134,58,86,74,106,44,68,52,76,40,56,48
%N A209637 Matula-numbers computed for rooted trees encoded by A071162 when interpreted in once-halved bit-tuple format.
%C A209637 Sequence A209638 gives the same terms sorted into ascending order.
%D A209637 Mueller, Szymanski, Knop and Trinajstic, A Comparison between the Matula Numbers and Bit-tuple Notation for Rooted Trees J. Chem. Inf. Comput. Sci. 1995, 35, pp. 211--213.
%F A209637 a(n) = A209636(A054429(n)) = A127301(A057505(A071163(n))) = A127301(A057163(A071163(n))).
%o A209637 (Python)
%o A209637 from sympy import prime
%o A209637 from mpmath import log
%o A209637 def a054429(n): return 3*(2**int(log(n, 2))) - (n + 1)
%o A209637 def a209636(n):
%o A209637     n = 2*n
%o A209637     m = 1
%o A209637     if n<2: return 1
%o A209637     while n>1:
%o A209637         if n%2==0:
%o A209637             n/=2
%o A209637             m*=2
%o A209637         else:
%o A209637             n=(n - 1)/2
%o A209637             m=prime(m)
%o A209637     return m
%o A209637 def a(n): return 1 if n==0 else a209636(a054429(n)) # _Indranil Ghosh_, May 26 2017
%K A209637 nonn,easy
%O A209637 0,2
%A A209637 _Antti Karttunen_, Mar 11 2012