cp's OEIS Frontend

A356353 Numbers k such that A356352(k) <> 1.

%I A356353 #13 Oct 17 2022 07:07:43
%S A356353 0,3,7,12,15,31,48,51,56,60,63,127,192,195,204,207,240,243,252,255,
%T A356353 448,455,504,511,768,771,780,783,816,819,828,831,960,963,972,975,992,
%U A356353 1008,1011,1020,1023,2047,3072,3075,3084,3087,3120,3123,3132,3135,3264,3267
%N A356353 Numbers k such that A356352(k) <> 1.
%C A356353 Also, numbers whose binary expansions are juxtapositions of constant blocks of size g > 1.
%C A356353 A001196 and A097254 are subsequences.
%C A356353 There are A178472(k) terms with binary length k.
%H A356353 Rémy Sigrist, <a href="/A356353/a356353.gp.txt">PARI program</a>
%H A356353 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A356353 The first terms, alongside their binary expansions and A356352(a(n)), are:
%e A356353   n   a(n)  bin(a(n))   A356352(a(n))
%e A356353   --  ----  ----------  -------------
%e A356353    1     0           0              0
%e A356353    2     3          11              2
%e A356353    3     7         111              3
%e A356353    4    12        1100              2
%e A356353    5    15        1111              4
%e A356353    6    31       11111              5
%e A356353    7    48      110000              2
%e A356353    8    51      110011              2
%e A356353    9    56      111000              3
%e A356353   10    60      111100              2
%e A356353   11    63      111111              6
%e A356353   12   127     1111111              7
%e A356353   13   192    11000000              2
%e A356353   14   195    11000011              2
%e A356353   15   204    11001100              2
%e A356353   16   207    11001111              2
%o A356353 (PARI) is(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); gcd(r)!=1 }
%o A356353 (PARI) See Links section.
%o A356353 (Python)
%o A356353 from math import gcd
%o A356353 from itertools import groupby
%o A356353 def ok(n):
%o A356353     if n == 0: return True # by convention of A356352
%o A356353     return gcd(*(len(list(g)) for k, g in groupby(bin(n)[2:]))) != 1
%o A356353 print([k for k in range(3268) if ok(k)]) # _Michael S. Branicky_, Oct 15 2022
%Y A356353 Cf. A001196, A097254, A178472, A356352.
%K A356353 nonn,base
%O A356353 1,2
%A A356353 _Rémy Sigrist_, Oct 15 2022