A065561 -id:A065561 - cp's OEIS frontend

A065578 Inverse permutation to A065561.

1, 2, 3, 5, 4, 7, 11, 6, 9, 8, 13, 10, 17, 19, 14, 12, 15, 23, 16, 29, 21, 18, 22, 20, 25, 31, 26, 27, 37, 24, 41, 28, 33, 34, 32, 30, 35, 43, 38, 39, 47, 53, 36, 46, 49, 40, 44, 42, 45, 59, 51, 61, 50, 55, 52, 48, 57, 58, 67, 54, 71, 56, 62, 65

Offset: 1

N. J. A. Sloane, Nov 29 2001

nonn

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

Index entries for sequences that are permutations of the natural numbers

More terms from John W. Layman, Dec 11 2001

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).

Original entry on oeis.org

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

Leroy Quet, Nov 29 2001

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

			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).

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

Cf. A002260, A065579, A065561.

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 *)

cp's OEIS Frontend

A065578 Inverse permutation to A065561.

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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).

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