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

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, 34, 26, 38, 20, 28, 24, 32, 127, 277, 179, 331, 109, 191, 157, 241, 79, 139, 101, 163, 71, 107, 89, 131, 62, 118, 82, 134, 58, 86, 74, 106, 44, 68, 52, 76, 40, 56, 48

Offset: 0

Author

Antti Karttunen, Mar 11 2012

Keywords

• nonn
• easy

Comments

Sequence A209638 gives the same terms sorted into ascending order.

References

• 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.

Programs

Python

from sympy import prime
from mpmath import log
def a054429(n): return 3*(2**int(log(n, 2))) - (n + 1)
def a209636(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
def a(n): return 1 if n==0 else a209636(a054429(n)) # Indranil Ghosh, May 26 2017

Formula

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