A325909 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n divides Sum_{k = 1..n} (-1)^k * a(k).

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.

Links

Table of n, a(n) for n=1..66.

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

Adjacent sequences: A325906 A325907 A325908 * A325910 A325911 A325912

Keyword

nonn

Author

Rémy Sigrist, Sep 08 2019

Status

approved