cp's OEIS Frontend

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

%I A348111 #11 Oct 09 2021 06:30:23
%S A348111 0,1,7,14,28,112,127,254,509,1016,1018,1792,2033,2037,2039,4066,4072,
%T A348111 4075,4078,8132,8135,8150,8156,16256,16300,16313,32513,32528,32576,
%U A348111 32601,32607,32626,32639,32767,65027,65087,65153,65202,65248,65253,65255,65534,130307
%N A348111 Numbers k whose binary expansion starts with the concatenation of the binary expansions of the run lengths in binary expansion of k.
%C A348111 We consider here that 0 has an empty binary expansion, and include it in the sequence.
%C A348111 This sequence is infinite as it contains A077585.
%H A348111 Rémy Sigrist, <a href="/A348111/b348111.txt">Table of n, a(n) for n = 1..10000</a>
%H A348111 Rémy Sigrist, <a href="/A348111/a348111.gp.txt">PARI program for A348111</a>
%e A348111 Regarding 32607:
%e A348111 - the binary expansion of 32607 is "111111101011111",
%e A348111 - the corresponding run lengths are: 7, 1, 1, 1, 5,
%e A348111 - in binary: "111", "1", "1", "1", "101",
%e A348111 - after concatenation: "111111101",
%e A348111 - as "111111101011111" starts with "111111101", 32607 belongs to this sequence.
%o A348111 (PARI) See Links section.
%o A348111 (Python)
%o A348111 from itertools import groupby
%o A348111 def ok(n):
%o A348111     if n == 0: return True
%o A348111     b = bin(n)[2:]
%o A348111     c = "".join(bin(len(list(g)))[2:] for k, g in groupby(b))
%o A348111     return b.startswith(c)
%o A348111 print(list(filter(ok, range(2**17)))) # _Michael S. Branicky_, Oct 02 2021
%Y A348111 Cf. A077585, A101211, A175930, A319678.
%K A348111 nonn,base
%O A348111 1,3
%A A348111 _Rémy Sigrist_, Oct 01 2021