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.

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

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: A023131 A375559 A356625 * A152201 A265579 A336879

Adjacent sequences: A026273 A026274 A026275 * A026277 A026278 A026279

Keyword

nonn

Author

Clark Kimberling

Status

approved