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A209636
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Matula-numbers computed for rooted trees encoded by A071162/A071163.
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8
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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, 37, 43, 29, 67, 41, 59, 31, 64, 48, 56, 40, 76, 52, 68, 44, 106, 74, 86, 58, 134, 82, 118, 62, 131, 89, 107, 71, 163, 101, 139, 79, 241, 157, 191, 109, 331, 179, 277
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OFFSET
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0,2
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COMMENTS
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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.
Sequence A209638 gives the same terms sorted into ascending order.
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LINKS
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FORMULA
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PROG
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(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))))))
(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
(Python)
from sympy import prime
def a(n):
n = 2*n
m = 1
if n<2: return 1
while n>1:
if n%2==0:
n//=2
m*=2
else:
n=(n - 1)//2
m=prime(m)
return m
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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