A065562 a(n) = b(n)-th highest positive integer not equal to any a(k), 1 <= k < n, where {b(n)} = 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, ... (sequence A002260).

1, 2, 4, 3, 6, 8, 5, 9, 11, 13, 7, 12, 15, 17, 19, 10, 16, 20, 22, 24, 26, 14, 21, 25, 28, 30, 32, 34, 18, 27, 31, 35, 37, 39, 41, 43, 23, 33, 38, 42, 45, 47, 49, 51, 53, 29, 40, 46, 50, 54, 56, 58, 60, 62, 64, 36, 48, 55, 59, 63, 66, 68, 70, 72, 74, 76, 44, 57, 65, 69, 73, 77

Offset: 1

Author

Leroy Quet, Nov 29 2001

Keywords

• easy
• nonn

Comments

Every positive integer occurs once and only once somewhere in this sequence.

Examples

			b(6) = 3, so a(6) = 8 = 3rd-highest positive integer not equal to 1, 2, 4, 3, or 6 (the values of a(k), 1 <= k < 6).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A002260, A065579, A065561.

Programs

Mathematica

Block[{a = {1}, s = Rest@ Range[96], r}, r = Flatten@ Map[Range, {1}~Join~Differences@ Most@ Reap[Do[If[Sow[PolygonalNumber@ i] > Last@ s, Break[]], {i, Infinity}]][[-1, 1]] ]; Do[AppendTo[a, s[[r[[i]] ]]]; s = Complement[s, a], {i, 2, 3 Max[s]/4}]; a] (* Michael De Vlieger, Sep 23 2017 *)