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A026276 a(n) = a(m) if a(m) has already occurred exactly once and n = a(m) + m + 2, else a(n) = least positive integer that has not yet occurred. 4
1, 2, 3, 1, 4, 2, 5, 3, 6, 7, 4, 8, 9, 5, 10, 11, 6, 12, 7, 13, 14, 8, 15, 9, 16, 17, 10, 18, 11, 19, 20, 12, 21, 22, 13, 23, 14, 24, 25, 15, 26, 27, 16, 28, 17, 29, 30, 18, 31, 32, 19, 33, 20, 34, 35, 21, 36, 22, 37, 38, 23, 39, 40, 24, 41, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Bob Selcoe, Mar 21 2017: (Start)

The sequence is composed of two unevenly interleaved subsequences B = {1..i} and C = {1..j}:

  n:  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20

  B:  1  2  3  -  4  -  5  -  6   7   -   8   9   -  10  11   -  12   -  13

  C:  -  -  -  1  -  2  -  3  -   -   4   -   -   5   -   -   6   -   7   -

Terms in C can be derived from B: b(n) = n when n <= 3; when n > 3 and b(n) is not null, then b(n) = c(n+b(n)+2). So for example, c(17) = 6 because b(9) = 6 and 9+6+2 = 17.

b(n) = c(5n/3) as n -> inf.; that is, when a(n) = j first appears, the second appearance approaches a(5n/3) as n -> inf. (End)

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

MATHEMATICA

a = {1}; Do[AppendTo[a, If[n == # + Position[a, #][[1, 1]] + 2, #, If[Length@ # == 0, Max@ a + 1, First@ #] &@ Complement[Range@ Max@ a, a]]] &@ Last@ SelectFirst[Transpose@ {Values@ #, Keys@ #}, Length@ First@ # == 1 &] &@ PositionIndex[a], {n, 2, 66}]; a (* Michael De Vlieger, Mar 22 2017, Version 10 *)

CROSSREFS

Cf. A009947.

Sequence in context: A118276 A023123 A023131 * A152201 A265579 A336879

Adjacent sequences:  A026273 A026274 A026275 * A026277 A026278 A026279

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified May 22 13:12 EDT 2022. Contains 353950 sequences. (Running on oeis4.)