A209636 Matula-numbers computed for rooted trees encoded by A071162/A071163.

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

Offset: 0

Author

Antti Karttunen, Mar 11 2012

Keywords

• nonn
• easy
• base
• look

Comments

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.

Links

• Indranil Ghosh (terms 0..1000) & Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to Matula-Goebel numbers

Crossrefs

Cf. A000040, A054429, A071162, A071163, A127301, A209637, A278541.

Programs

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
print([a(n) for n in range(101)]) # Indranil Ghosh, May 25 2017, translated from Antti Karttunen's SCHEME code

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))))))

Formula

a(n) = A127301(A071163(n)) = A209637(A054429(n)).