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A325909
Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n divides Sum_{k = 1..n} (-1)^k * a(k).
0
1, 3, 2, 4, 9, 5, 7, 15, 8, 10, 21, 11, 13, 27, 14, 16, 33, 17, 19, 39, 20, 22, 45, 23, 25, 51, 26, 28, 57, 29, 31, 63, 32, 34, 69, 35, 37, 75, 38, 40, 81, 41, 43, 87, 44, 46, 93, 47, 49, 99, 50, 52, 105, 53, 55, 111, 56, 58, 117, 59, 61, 123, 62, 64, 129, 65
OFFSET
1,2
COMMENTS
This sequence has similarities with A019444: here we have partial alternating sums, there partial sums.
FORMULA
Apparently:
- a(3*k) = 3*k - 1,
- a(3*k+1) = 3*k + 1,
- a(3*k+2) = 6*k + 3.
EXAMPLE
The first terms, alongside the corresponding partial alternating sums, are:
n a(n) S_n
-- ---- ---
1 1 -1
2 3 2
3 2 0
4 4 4
5 9 -5
6 5 0
7 7 -7
8 15 8
9 8 0
10 10 10
11 21 -11
12 11 0
PROG
(PARI) s=t=0; for (n=1, 66, for (v=1, oo, if (!bittest(s, v) && (tt=t+v*(-1)^n)%n==0, print1 (v ", "); t=tt; s+=2^v; break)))
CROSSREFS
Cf. A019444.
Sequence in context: A201838 A099257 A374789 * A270701 A083762 A173028
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Sep 08 2019
STATUS
approved