A348111 Numbers k whose binary expansion starts with the concatenation of the binary expansions of the run lengths in binary expansion of k.

0, 1, 7, 14, 28, 112, 127, 254, 509, 1016, 1018, 1792, 2033, 2037, 2039, 4066, 4072, 4075, 4078, 8132, 8135, 8150, 8156, 16256, 16300, 16313, 32513, 32528, 32576, 32601, 32607, 32626, 32639, 32767, 65027, 65087, 65153, 65202, 65248, 65253, 65255, 65534, 130307

Offset

1,3

Comments

We consider here that 0 has an empty binary expansion, and include it in the sequence.

This sequence is infinite as it contains A077585.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A348111

Example

Regarding 32607:
- the binary expansion of 32607 is "111111101011111",
- the corresponding run lengths are: 7, 1, 1, 1, 5,
- in binary: "111", "1", "1", "1", "101",
- after concatenation: "111111101",
- as "111111101011111" starts with "111111101", 32607 belongs to this sequence.

Prog

(PARI) See Links section.
(Python)
from itertools import groupby
def ok(n):
    if n == 0: return True
    b = bin(n)[2:]
    c = "".join(bin(len(list(g)))[2:] for k, g in groupby(b))
    return b.startswith(c)
print(list(filter(ok, range(2**17)))) # Michael S. Branicky, Oct 02 2021

Crossrefs

Cf. A077585, A101211, A175930, A319678.

Sequence in context: A005009 A135092 A245417 * A332371 A058530 A293359

Adjacent sequences: A348108 A348109 A348110 * A348112 A348113 A348114

Keyword

nonn,base

Author

Rémy Sigrist, Oct 01 2021

Status

approved