A300950 Fixed points of A300948.

3, 4, 7, 8, 11, 12, 15, 48, 51, 52, 55, 56, 59, 60, 63, 64, 67, 68, 71, 72, 75, 76, 79, 112, 115, 116, 119, 120, 123, 124, 127, 128, 131, 132, 135, 136, 139, 140, 143, 176, 179, 180, 183, 184, 187, 188, 191, 192, 195, 196, 199, 200, 203, 204, 207, 240, 243

Offset: 1

Author

Rémy Sigrist, Mar 16 2018

Keywords

• nonn
• base

Comments

This sequence contains A007013(k) for any k > 0.

We can devise a set of primitive fixed points of A300948, say P, as follows:

- P contains the powers of 2, say 2^i, such that A300948(2^i) = 2^i (in that case, i = a(k)-1 for some k > 0),

- and the sums of two distinct powers of 2, say 2^i + 2^j, such that A300948(2^i) = 2^j,

- we can uniquely write any term of this sequence as a sum of distinct terms of P.

Examples

			A300948(7) = 7 hence 7 belongs to this sequence.
A300948(42) = 25 hence 42 does not belong to this sequence.
		

Crossrefs

Cf. A007013, A300948.

Formula

For any n > 0 with binary expansion Sum_{i=0..k} b_i * 2^i, a(n) = Sum_{i=0..k} b_i * p(i+1) (where p(i) denotes the i-th term of the set P described in the Comments section).