A352889 - OEIS

%I #11 Apr 07 2022 13:20:47

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A352889/b352889.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

%e    n   A109812(n)  [in base-2]   a(n) = number of runs

%e -----+-------------------------------------------------

%e    1 |          1       [1],      1

%e    2 |          2      [10],      2

%e    3 |          4     [100],      2

%e    4 |          3      [11],      1

%e    5 |          8    [1000],      2

%e    6 |          5     [101],      3

%e    7 |         10    [1010],      4

%e    8 |         16   [10000],      2

%e    9 |          6     [110],      2

%e   10 |          9    [1001],      3

%e   11 |         18   [10010],      4

%o (PARI)

%o v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '

%o up_to = #v109812;

%o A109812(n) = v109812[n];

%o A352889(n) = A005811(A109812(n));

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

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Apr 07 2022