A286633 Base-3 {digit+1} product of A254103: a(n) = A006047(A254103(n)).

1, 2, 3, 2, 6, 4, 9, 3, 12, 2, 6, 6, 18, 8, 18, 4, 24, 12, 27, 6, 12, 3, 9, 4, 36, 4, 12, 6, 36, 2, 6, 12, 48, 6, 18, 12, 54, 16, 36, 9, 24, 24, 54, 4, 18, 8, 18, 6, 72, 24, 54, 6, 24, 12, 27, 6, 72, 36, 81, 12, 12, 6, 18, 18, 96, 36, 81, 12, 36, 6, 18, 36, 108, 8, 24, 18, 72, 24, 54, 8, 48, 12, 36, 18, 108, 2, 6, 24, 36, 4, 12, 12, 36, 3, 9, 4

Offset: 0

Author

Antti Karttunen, Jun 03 2017

Keywords

• nonn
• base

Comments

Reflecting the structure of A254103 also this sequence can be represented as a binary tree:

1

|

...................2...................

3 2

6......../ \........4 9......../ \........3

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

12 2 6 6 18 8 18 4

24 12 27 6 12 3 9 4 36 4 12 6 36 2 6 12

etc.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A000079, A006047, A042950, A254103, A286586, A286587, A286632.

Programs

Python

from sympy.ntheory.factor_ import digits
from operator import mul
from functools import reduce
def a006047(n):
    d=digits(n, 3)
    return reduce(mul, [1 + d[i] for i in range(1, len(d))])
def a254103(n):
    if n==0: return 0
    if n%2==0: return 3*a254103(n//2) - 1
    else: return (3*(1 + a254103((n - 1)//2)))//2
def a(n): return a006047(a254103(n)) # Indranil Ghosh, Jun 06 2017

Scheme

(define (A286633 n) (A006047 (A254103 n)))

Formula

a(n) = A006047(A254103(n)).

For n >= 0, a(A000079(n)) = A042950(n).