cp's OEIS Frontend

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

%I A157261 #20 Oct 05 2024 20:00:19
%S A157261 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,
%T A157261 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,
%U A157261 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
%N A157261 A run-length encoding of blocks of 2 in A090822.
%C A157261 The assumption underlying this sequence is that the number 2 occurs isolated or in blocks of length 3 in A090822.
%C A157261 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.
%C A157261 This is equivalent to counting the successive triples of indices of the form k, k+1, k+2 in A157041.
%C A157261 Conjecture: This is not multiplicative. - _N. J. A. Sloane_, Jul 28 2018
%H A157261 Andrew Howroyd, <a href="/A157261/b157261.txt">Table of n, a(n) for n = 1..1727</a>
%e A157261 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).
%e A157261 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).
%e A157261 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.
%t A157261 nmax = 2000;
%t A157261 A090822 = Cases[Import["https://oeis.org/A090822/b090822.txt", "Table"], {_, _}][[1 ;; nmax, 2]];
%t A157261 Length /@ DeleteCases[Split[DeleteCases[Split[A090822], s_List /; s[[1]] != 2] , #1 == #2 == {2, 2, 2}&], {{2}}] (* _Jean-François Alcover_, Sep 02 2019 *)
%Y A157261 Cf. A090822, A157041.
%K A157261 nonn
%O A157261 1,4
%A A157261 _Paul Curtz_, Feb 26 2009
%E A157261 Edited by _R. J. Mathar_, Feb 27 2009