A321485 - OEIS

%I #11 Nov 14 2018 12:25:14

%S 10,11,12,13,14,15,16,17,18,19,110,21,112,113,114,115,116,117,118,119,

%T 120,121,22,123,124,125,126,127,128,129,130,131,132,23,134,135,136,

%U 137,138,139,140,141,142,143,24,145,146,147,148,149,150,151,152,153,154

%N Describe n from left to right in terms of blocks with the maximum number of repetitions (and then with the maximum size).

%C This sequence is a variant of the "Look and Say" sequence A045918 with features from Gijswijt's sequence A090822.

%C Any digit appearing in n also appears in a(n).

%H Rémy Sigrist, <a href="/A321485/b321485.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A321485/a321485.gp.txt">PARI program for A321485</a>

%F a((10^k-1)/9 * d) = 10*k + d for any k > 0 and d = 1..9.

%F A055642(a(n)) <= 1 + A055642(n).

%e The following table shows some examples with the corresponding blocks:

%e   n         a(n)    Blocks

%e   --------  ------  ---------------

%e          0      10              (0)

%e          1      11              (1)

%e         12     112             (12)

%e        100    1100            (100)

%e        111      31          (1|1|1)

%e      22123  221123       (2|2)(123)

%e     112211  212221  (1|1)(2|2)(1|1)

%e     212212    2212        (212|212)

%e   11221122   21122      (1122|1122)

%o (PARI) See Links section.

%Y Cf. A045918, A090822.

%K nonn,base

%O 0,1

%A _Rémy Sigrist_, Nov 11 2018