A327143 - OEIS

%I #40 Jan 15 2020 14:49:15

%S 1,2,4,3,5,7,9,6,8,2111110,2000001,11,13,15,17,20,22,24,111111110,210,

%T 10,11110,101,19,21,31,33,23,35,37,39,26,28,110,211110,12,14,103,51,

%U 2001,25,53,27,55,57,11112,212,40,16,42,1110,21110,44,111110,46,11111110,48,1111111110,21111110,2111111110,1112,18,112

%N Variation on Golomb's sequence starting with (1,2): a(n)=length of n-th run of both consecutive integers and consecutive digits with same parity.

%C Among the first 10000 terms the largest value is a(7898)=211111111111111111111111111110 and the smallest value not occurring is 29. - _Lars Blomberg_, Jan 10 2020

%H Lars Blomberg, <a href="/A327143/b327143.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence's start is reordered herunder in two ways: the first one to check the runs of consecutive integers, the second one to check the runs of consecutive digits.

%e Start = 1,2,4,3,5,7,9,6,8,2111110,2000001,11,13,15,17,...

%e #1 Golomb's variation (integers):

%e 1, --------------->  size 1 block of odd integers

%e 2,4, ------------->  size 2 block of even integers

%e 3,5,7,9, --------->  size 4 block of odd integers

%e 6,8,2111110, ----->  size 3 block of even integers

%e 2000001,11,13,15,17, size 5 block of odd integers

%e ...

%e #2 Golomb's variation (digits):

%e Start = 1,2,4,3,5,7,9,6,8,2111110,2000001,11,13,15,17,...

%e 1, ----> size 1 block of odd digits

%e 2,4, --> size 2 block of even digits

%e 3,5,7,9, size 4 block of odd digits

%e 6,8,2    size 3 block of even digits

%e 11111    size 5 block of odd digits

%e 0,200000 size 7 block of even digits

%e In both variations, the successive sizes rebuild the sequence.

%Y Cf. A093506 (Variation on Golomb's sequence starting with (1,2): a(n)=length of n-th run of consecutive integers with same parity).

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Lars Blomberg_, Jan 05 2020