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A302659 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, A065368(a(n) * a(n+1)) = 0. 1
1, 4, 2, 6, 8, 3, 12, 7, 16, 5, 24, 9, 28, 10, 14, 18, 20, 11, 32, 15, 44, 13, 36, 17, 40, 19, 52, 21, 48, 22, 26, 30, 34, 38, 42, 46, 50, 56, 23, 60, 25, 64, 27, 68, 29, 72, 31, 76, 35, 80, 33, 84, 37, 88, 41, 96, 43, 92, 39, 100, 45, 112, 47, 116, 49, 104 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For any base b > 1:
- let s_b be the alternate sum of digits in base b,
- in particular s_2 = A065359, s_3 = A065368 and s_10 = A225693,
- 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
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
Sequence in context: A114478 A367882 A330530 * A363705 A134239 A136390
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 11 2018
STATUS
approved

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Last modified June 23 10:25 EDT 2024. Contains 373629 sequences. (Running on oeis4.)