A055170 n-th distinct number to appear in A055168; also the n-th to appear in A217760.

0, 1, 2, 3, 4, 5, 6, 9, 7, 11, 8, 13, 17, 10, 19, 21, 15, 12, 23, 26, 20, 14, 16, 28, 22, 32, 24, 35, 27, 18, 38, 30, 25, 41, 34, 29, 44, 31, 48, 50, 46, 36, 52, 39, 42, 56, 37, 60, 54, 47, 33, 63, 58, 40, 43, 68, 53, 45, 72, 65, 76, 55, 61, 51

Offset

1,3

Comments

Conjecture: this sequence is a permutation of the nonnegative integers.

This is the limiting sequence of the noun-integers in the n-th segment generated as in A217760 (but not A055186); see Example.

The conjecture is true: the number 0 appears in every segment of A055168, and, for n > 0, n appears in the (n+1)-th segment (as the number of occurrences of 0 in the previous segments). - Rémy Sigrist, Oct 16 2017

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..6000

Example

Following the adjective-before-noun definition at A217760, the first segments are
0..1..2 1..3 3 1..4 5 2 2..5 6 5 3 1 1..6 9 6 5 2 4 1..
...0..0 1..0 1 2..0 1 2 3..0 1 2 3 4 5..0 1 2 3 4 5 6..
(continuing:)
7 11 8 6 4 6 4 1....8 13 9 7 7 7 5 2 1 1..1
0..1 2 3 4 5 6 9....0..1 2 3 4 5 6 9 7 11 8,
this last segment counting the "8 0's and 13 1's and 9 2's..." which have previously appeared.  The numbers 8, 13, 9 are used as adjectives and the numbers 0 1 2 3 4 5 6 9 7 11 8 (as in A055170) are used as nouns.

Mathematica

s = {0}; Do[s = Flatten[{s, {Count[s, #], #} & /@ (DeleteDuplicates[s])}], {30}]; DeleteDuplicates[s] (* Peter J. C. Moses, Mar 25 2013 *)

Crossrefs

Cf. A055168, A217760.

Sequence in context: A308007 A360413 A270194 * A068384 A222253 A353591

Adjacent sequences: A055167 A055168 A055169 * A055171 A055172 A055173

Keyword

nonn

Author

Clark Kimberling, Apr 27 2000

Extensions

Corrected and edited by Clark Kimberling, Oct 24 2009

Reconciled to A217760 (formerly A055186) by Clark Kimberling, Mar 25 2013

Status

approved