A343963 - OEIS

%I #6 May 08 2021 23:07:36

%S 0,1,2,7,9,22,55,121,137,310,695,1529,3209,6966,15031,32249,34297,

%T 72841,154422,326327,687609,1410553,2956425,6183734,12909239,26902009,

%U 55936505,116202633,241064758,499448503,1033534969,2136311289,2203420153,4545387657

%N a(0) = 0, and for any n > 0, the binary expansion of n has n digits and starts with the binary expansion of n, say of w digits, and in case n > w, the remaining binary digits in a(n) are those of a(n-w).

%C To build the binary expansion of a(n):

%C - start with n indeterminate digits,

%C - while there are some, say m, indeterminate digits,

%C   replace the first of them with the binary expansion of m.

%C The binary plot of the sequence has locally periodic patterns.

%H Rémy Sigrist, <a href="/A343963/a343963.png">Binary plot of the sequence for n <= 2^10</a>

%F A070939(a(n)) = n for any n > 0.

%e For n = 10:

%e - the binary expansion of a(10) has 10 digits, and is the concatenation of:

%e    - the binary expansion of 10 which is "1010",

%e    - the binary expansion of 10 - 4 = 6 which is "110",

%e    - the binary expansion of 10 - 4 - 3 = 3 which is "11",

%e    - the binary expansion of 10 - 4 - 3 - 2 = 1 which is "1",

%e    - as 10 = 4 + 3 + 2 + 1, we stop here,

%e - so the binary expansion of a(10) is "1010110111",

%e - and a(10) = 695.

%o (PARI) a(n) = { if (n==0, 0, my (k=n-#binary(n)); n*2^k+a(k)) }

%Y Cf. A070939, A319678.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, May 05 2021