A286632 Base-3 digit sum of A254103: a(n) = A053735(A254103(n)).

0, 1, 2, 1, 3, 2, 4, 2, 4, 1, 3, 3, 5, 3, 5, 2, 5, 4, 6, 3, 4, 2, 4, 2, 6, 2, 4, 3, 6, 1, 3, 4, 6, 3, 5, 4, 7, 4, 6, 4, 5, 5, 7, 2, 5, 3, 5, 3, 7, 5, 7, 3, 5, 4, 6, 3, 7, 6, 8, 4, 4, 3, 5, 5, 7, 6, 8, 4, 6, 3, 5, 6, 8, 3, 5, 5, 7, 5, 7, 3, 6, 4, 6, 5, 8, 1, 3, 5, 6, 2, 4, 4, 6, 2, 4, 2, 8, 4, 6, 6, 8, 2, 4, 2, 6, 3, 5, 4, 7, 4, 6, 5, 8, 5, 7, 5, 9, 5, 7, 4, 5

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:

0

|

...................1...................

2 1

3......../ \........2 4......../ \........2

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

4 1 3 3 5 3 5 2

5 4 6 3 4 2 4 2 6 2 4 3 6 1 3 4

etc.

Links

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

Crossrefs

Cf. A053735, A254103, A286585, A286633.

Programs

Python

from sympy.ntheory.factor_ import digits
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 sum(digits(a254103(n), 3)[1:]) # Indranil Ghosh, Jun 06 2017

Scheme

(define (A286632 n) (A053735 (A254103 n)))

Formula

a(n) = A053735(A254103(n)).

a(n) = A056239(A286633(n)).

For all n >= 0, a(A000079(n)) = n+1.