A157261 A run-length encoding of blocks of 2 in A090822.

1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 10, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 3

Offset

1,4

Comments

The assumption underlying this sequence is that the number 2 occurs isolated or in blocks of length 3 in A090822.

This sequence notes the size of successive blocks of length 3, that is, the number of blocks of length 3 not interrupted by an isolated 2.

This is equivalent to counting the successive triples of indices of the form k, k+1, k+2 in A157041.

Conjecture: This is not multiplicative. - N. J. A. Sloane, Jul 28 2018

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1727

Example

A090822(n)=2 at n=3 (isolated), n=6-8 (block), n=12 (isolated), n=15-17 (block), n=19 (isolated), n=22 (isolated), n=25-27 (block), n=31 (isolated), n=34-36 (block), n=38-40 (block), n=42-44 (block), n=47 (isolated).
Determining the cluster size of successive blocks, we write a(1)=1 (block at n>=6), a(2)=1 (block at n>=15), a(3)=1 (block at n>=25), a(4)=3 (blocks at n>=34, n>=38, n>=42), a(5)=1 (block at n>=53).
a(16)=9 represents the 9 blocks at n>=179, n>=183, n>=187, n>=192, n>=196, n>=200,... n>=213, followed by an isolated 2 at n=223.

Mathematica

nmax = 2000;
A090822 = Cases[Import["https://oeis.org/A090822/b090822.txt", "Table"], {_, _}][[1 ;; nmax, 2]];
Length /@ DeleteCases[Split[DeleteCases[Split[A090822], s_List /; s[[1]] != 2] , #1 == #2 == {2, 2, 2}&], {{2}}] (* Jean-François Alcover, Sep 02 2019 *)

Crossrefs

Cf. A090822, A157041.

Sequence in context: A130605 A354872 A368335 * A079110 A079619 A318577

Adjacent sequences: A157258 A157259 A157260 * A157262 A157263 A157264

Keyword

nonn

Author

Paul Curtz, Feb 26 2009

Extensions

Edited by R. J. Mathar, Feb 27 2009

Status

approved