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%I #25 Mar 30 2021 01:39:17
%S 1,2,4,3,8,6,7,5,16,12,14,10,19,13,17,11,32,24,28,20,38,26,34,22,53,
%T 37,43,29,67,41,59,31,64,48,56,40,76,52,68,44,106,74,86,58,134,82,118,
%U 62,131,89,107,71,163,101,139,79,241,157,191,109,331,179,277
%N Matula-numbers computed for rooted trees encoded by A071162/A071163.
%C Sequence is injective: Any number occurs at most once, as each plane tree encoded by A071162/A071163 is mapped to a unique non-oriented rooted tree. See also A209637, A209638.
%C Sequence A209638 gives the same terms sorted into ascending order.
%H Indranil Ghosh (terms 0..1000) & Antti Karttunen, <a href="/A209636/b209636.txt">Table of n, a(n) for n = 0..8191</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>
%F a(n) = A127301(A071163(n)) = A209637(A054429(n)).
%o (Scheme) (define (A209636 n) (let loop ((n (* 2 n)) (m 1)) (cond ((< n 2) m) ((even? n) (loop (/ n 2) (* m 2))) (else (loop (/ (- n 1) 2) (A000040 m))))))
%o (PARI) A209636(n) = { my(n=2*n, m=1); while(n >= 2, if(!(n%2),m*=2,m = prime(m)); n\=2); m; } \\ _Antti Karttunen_, May 25 2017
%o (Python)
%o from sympy import prime
%o def a(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 print([a(n) for n in range(101)]) # _Indranil Ghosh_, May 25 2017, translated from _Antti Karttunen_'s SCHEME code
%Y Cf. A000040, A054429, A071162, A071163, A127301, A209637, A278541.
%K nonn,easy,base,look
%O 0,2
%A _Antti Karttunen_, Mar 11 2012
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