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

1,1

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.

Links

Table of n, a(n) for n=1..57.

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).

Example

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

Crossrefs

Cf. A007013, A300948.

Sequence in context: A188259 A058235 A107819 * A368083 A067186 A133675

Adjacent sequences: A300947 A300948 A300949 * A300951 A300952 A300953

Keyword

nonn,base

Author

Rémy Sigrist, Mar 16 2018

Status

approved