OFFSET
1,2
COMMENTS
For any base b > 1:
- let s_b be the alternate sum of digits in base b,
- we can build an analog of this sequence, say f_b, by considering s_b instead of A065368,
- f_b is well defined: for any k > 0, s_b(k * (1 + b^(2*i + 1))) = 0 whenever k < b^(2*i + 1), hence we can always extend the sequence,
- f_b is conjectured to be a permutation of the natural numbers,
- the scatterplot of f_b shows lines that seem related to the value of s_b(f_b) mod b+1.
See A302544 for a similar sequence.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored scatterplot of the first 10000 terms
Rémy Sigrist, Scatterplot of the first 10000 of f_2
Rémy Sigrist, Scatterplot of the first 10000 of f_5
Rémy Sigrist, PARI program for A302659
EXAMPLE
The first terms, alongside the ternary representation of a(n) * a(n+1), are:
n a(n) tern(a(n) * a(n+1))
-- ---- -------------------
1 1 11
2 4 22
3 2 110
4 6 1210
5 8 220
6 3 1100
7 12 10010
8 7 11011
9 16 2222
10 5 11110
11 24 22000
12 9 100100
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 11 2018
STATUS
approved