A343963 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).

0, 1, 2, 7, 9, 22, 55, 121, 137, 310, 695, 1529, 3209, 6966, 15031, 32249, 34297, 72841, 154422, 326327, 687609, 1410553, 2956425, 6183734, 12909239, 26902009, 55936505, 116202633, 241064758, 499448503, 1033534969, 2136311289, 2203420153, 4545387657

Offset

0,3

Comments

To build the binary expansion of a(n):

- start with n indeterminate digits,

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

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

The binary plot of the sequence has locally periodic patterns.

Links

Table of n, a(n) for n=0..33.

Rémy Sigrist, Binary plot of the sequence for n <= 2^10

Formula

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

Example

For n = 10:
- the binary expansion of a(10) has 10 digits, and is the concatenation of:
   - the binary expansion of 10 which is "1010",
   - the binary expansion of 10 - 4 = 6 which is "110",
   - the binary expansion of 10 - 4 - 3 = 3 which is "11",
   - the binary expansion of 10 - 4 - 3 - 2 = 1 which is "1",
   - as 10 = 4 + 3 + 2 + 1, we stop here,
- so the binary expansion of a(10) is "1010110111",
- and a(10) = 695.

Prog

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

Crossrefs

Cf. A070939, A319678.

Sequence in context: A293646 A020895 A174247 * A321322 A343495 A065139

Adjacent sequences: A343960 A343961 A343962 * A343964 A343965 A343966

Keyword

nonn,base

Author

Rémy Sigrist, May 05 2021

Status

approved