login
A286633
Base-3 {digit+1} product of A254103: a(n) = A006047(A254103(n)).
5
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
0,2
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
FORMULA
a(n) = A006047(A254103(n)).
For n >= 0, a(A000079(n)) = A042950(n).
PROG
(Scheme) (define (A286633 n) (A006047 (A254103 n)))
(Python)
from sympy.ntheory.factor_ import digits
from operator import mul
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 floor((3*(1 + a254103((n - 1)/2)))/2)
def a(n): return a006047(a254103(n)) # Indranil Ghosh, Jun 06 2017
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Jun 03 2017
STATUS
approved