

A157261


A runlength encoding of blocks of 2 in A090822.


2



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
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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=67 (block), n=12 (isolated), n=1517 (block), n=19 (isolated), n=22 (isolated), n=2527 (block), n=31 (isolated) n=3436 (block), n=3840 (block), n=4244 (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}}] (* JeanFrançois Alcover, Sep 02 2019 *)


CROSSREFS

Cf. A090822, A157041.
Sequence in context: A195644 A143632 A130605 * 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



