cp's OEIS Frontend

A330036 The length of the largest run of 0's in the binary expansion of n + the length of the largest run of 1's in the binary expansion of n.

%I A330036 #30 Apr 06 2020 12:31:37
%S A330036 1,1,2,2,3,2,3,3,4,3,2,3,4,3,4,4,5,4,3,4,3,2,3,4,5,4,3,3,5,4,5,5,6,5,
%T A330036 4,5,3,3,4,5,4,3,2,3,4,3,4,5,6,5,4,4,4,3,3,4,6,5,4,4,6,5,6,6,7,6,5,6,
%U A330036 4,4,5,6,4,3,3,4,4,4,5,6,5,4,3
%N A330036 The length of the largest run of 0's in the binary expansion of n + the length of the largest run of 1's in the binary expansion of n.
%C A330036 All numbers appear in this sequence. The number of 1's in the n-th Mersenne number (A000225) is n and the number of 0's in the n-th Mersenne number is 0. 0+n=n. See formula.
%H A330036 Robert Israel, <a href="/A330036/b330036.txt">Table of n, a(n) for n = 0..10000</a>
%F A330036 a(n) = A087117(n) + A038374(n).
%F A330036 a(A000225(n)) = n for n > 0.
%e A330036    n [binary n ]  A087117(n) + A038374(n) = a(n)
%e A330036    0 [       0 ]  1          + 0          = 1
%e A330036    1 [       1 ]  0          + 1          = 1
%e A330036    2 [     1 0 ]  1          + 1          = 2
%e A330036    3 [     1 1 ]  0          + 2          = 2
%e A330036    4 [   1 0 0 ]  2          + 1          = 3
%e A330036    5 [   1 0 1 ]  1          + 1          = 2
%e A330036    6 [   1 1 0 ]  1          + 2          = 3
%e A330036    7 [   1 1 1 ]  0          + 3          = 3
%e A330036    8 [ 1 0 0 0 ]  3          + 1          = 4
%e A330036    9 [ 1 0 0 1 ]  2          + 1          = 3
%e A330036   10 [ 1 0 1 0 ]  1          + 1          = 2
%e A330036   11 [ 1 0 1 1 ]  1          + 2          = 3
%e A330036   12 [ 1 1 0 0 ]  2          + 2          = 4
%e A330036   13 [ 1 1 0 1 ]  1          + 2          = 3
%e A330036   14 [ 1 1 1 0 ]  1          + 3          = 4
%e A330036   15 [ 1 1 1 1 ]  0          + 4          = 4
%p A330036 f:= proc(n) local L;
%p A330036   L:= convert(n,base,2);
%p A330036   max(map(nops,[ListTools:-Split(`=`,L,1)]))+max(map(nops,[ListTools:-Split(`=`,L,0)]))
%p A330036 end proc:
%p A330036 map(f, [$0..100]); # _Robert Israel_, Apr 06 2020
%t A330036 Table[Sum[Max[Differences[Position[Flatten@{k,IntegerDigits[n,2],k},k]]],{k,0,1}]-2,{n,0,82}]
%Y A330036 Cf. A000120, A000225, A007088, A023416, A038374, A087117.
%K A330036 nonn,base
%O A330036 0,3
%A A330036 _Joshua Oliver_, Nov 27 2019