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

Author

Clark Kimberling

Keywords

• nonn

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

Crossrefs

Cf. A009947.

Programs

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 *)