A352889 Number of runs in the binary expansion of A109812(n).

1, 2, 2, 1, 2, 3, 4, 2, 2, 3, 4, 2, 3, 2, 2, 1, 2, 3, 4, 3, 4, 3, 4, 5, 4, 3, 2, 1, 2, 4, 5, 4, 3, 4, 3, 4, 5, 4, 3, 2, 3, 4, 3, 2, 3, 4, 4, 3, 4, 2, 3, 4, 3, 2, 3, 4, 5, 6, 4, 6, 5, 4, 5, 4, 6, 3, 4, 2, 3, 4, 3, 4, 3, 2, 2, 1, 4, 5, 4, 5, 6, 5, 4, 3, 4, 5, 4, 3, 4, 5, 6, 7, 6, 5, 6, 4, 5, 2, 5, 4, 4, 3, 2, 3, 4

Offset: 1

Author

Antti Karttunen, Apr 07 2022

Keywords

• nonn
• base

Examples

			   n   A109812(n)  [in base-2]   a(n) = number of runs
-----+-------------------------------------------------
   1 |          1       [1],      1
   2 |          2      [10],      2
   3 |          4     [100],      2
   4 |          3      [11],      1
   5 |          8    [1000],      2
   6 |          5     [101],      3
   7 |         10    [1010],      4
   8 |         16   [10000],      2
   9 |          6     [110],      2
  10 |          9    [1001],      3
  11 |         18   [10010],      4
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A005811, A109812, A352575, A352884, A352888.

Programs

PARI

v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '
up_to = #v109812;
A109812(n) = v109812[n];
A352889(n) = A005811(A109812(n));

Formula

a(n) = A005811(A109812(n)).