A361838 a(n) is the number of 2s in the binary hereditary representation of 2n.

1, 2, 3, 2, 3, 4, 5, 3, 4, 5, 6, 5, 6, 7, 8, 3, 4, 5, 6, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 11, 4, 5, 6, 7, 6, 7, 8, 9, 7, 8, 9, 10, 9, 10, 11, 12, 7, 8, 9, 10, 9, 10, 11, 12, 10, 11, 12, 13, 12, 13, 14, 15, 4, 5, 6, 7, 6, 7, 8, 9, 7, 8, 9, 10, 9, 10, 11, 12, 7

Offset

1,2

Comments

See comments on A266201 for the definition of hereditary representation.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

A table of n, the binary hereditary representation of 2n, and the number of 2s in the representation:
 n | hereditary rep. of 2n   | number of 2s
---+-------------------------+--------------
 1 | 2                       |      1
 2 | 2^2                     |      2
 3 | 2^2+2                   |      3
 4 | 2^(2+1)                 |      2
 5 | 2^(2+1)+2               |      3
 6 | 2^(2+1)+2^2             |      4
 7 | 2^(2+1)+2^2+2           |      5
 8 | 2^2^2                   |      3
 9 | 2^2^2+2                 |      4
10 | 2^2^2+2^2               |      5
11 | 2^2^2+2^2+2             |      6
12 | 2^2^2+2^(2+1)           |      5
13 | 2^2^2+2^(2+1)+2         |      6
14 | 2^2^2+2^(2+1)+2^2       |      7
15 | 2^2^2+2^(2+1)+2^2+2     |      8
16 | 2^(2^2+1)               |      3
17 | 2^(2^2+1)+2             |      4
18 | 2^(2^2+1)+2^2           |      5
19 | 2^(2^2+1)+2^2+2         |      6
20 | 2^(2^2+1)+2^(2+1)       |      5
21 | 2^(2^2+1)+2^(2+1)+2     |      6
22 | 2^(2^2+1)+2^(2+1)+2^2   |      7
23 | 2^(2^2+1)+2^(2+1)+2^2+2 |      8
24 | 2^(2^2+1)+2^2^2         |      6
25 | 2^(2^2+1)+2^2^2+2       |      7
26 | 2^(2^2+1)+2^2^2+2^2     |      8
27 | 2^(2^2+1)+2^2^2+2^2+2   |      9
28 | 2^(2^2+1)+2^2^2+2^(2+1) |      8

Prog

(PARI) a(n)=if(n==0, 0, sum(k=0, logint(n, 2), if(bittest(n, k), 1 + a((k+1)\2)))) \\ Andrew Howroyd, Apr 07 2023

Crossrefs

Cf. A005245, A025280.

Sequence in context: A324532 A324390 A260112 * A213183 A125929 A309236

Adjacent sequences: A361835 A361836 A361837 * A361839 A361840 A361841

Keyword

nonn,base,hear

Author

Jodi Spitz, Mar 26 2023

Status

approved