A209637 - OEIS

%I #10 May 26 2017 08:55:08

%S 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 34,26,38,20,28,24,32,127,277,179,331,109,191,157,241,79,139,101,163,

%U 71,107,89,131,62,118,82,134,58,86,74,106,44,68,52,76,40,56,48

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

%C Sequence A209638 gives the same terms sorted into ascending order.

%D 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 a(n) = A209636(A054429(n)) = A127301(A057505(A071163(n))) = A127301(A057163(A071163(n))).

%o (Python)

%o from sympy import prime

%o from mpmath import log

%o def a054429(n): return 3*(2**int(log(n, 2))) - (n + 1)

%o def a209636(n):

%o     n = 2*n

%o     m = 1

%o     if n<2: return 1

%o     while n>1:

%o         if n%2==0:

%o             n/=2

%o             m*=2

%o         else:

%o             n=(n - 1)/2

%o             m=prime(m)

%o     return m

%o def a(n): return 1 if n==0 else a209636(a054429(n)) # _Indranil Ghosh_, May 26 2017

%K nonn,easy

%O 0,2

%A _Antti Karttunen_, Mar 11 2012