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%I #19 Feb 16 2024 14:39:34
%S 4,20,33,36,49,52,84,97,100,113,116,129,135,148,161,164,177,180,193,
%T 199,212,225,228,241,244,340,353,356,369,372,385,391,404,417,420,433,
%U 436,449,455,468,481,484,497,500,513,519,543,545,548,561,564,596,609,612
%N Numbers k such that 0 and 1 occur juxtaposed in the base-4 representation of k but not of k+1.
%t SequencePosition[Table[If[SequenceCount[IntegerDigits[n,4],{0,1}]>0 || SequenceCount[ IntegerDigits[ n,4],{1,0}]>0,1,0],{n,600}],{1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 14 2016 *)
%o (Python)
%o from sympy.ntheory.factor_ import digits
%o def has01or10(k):
%o s = "".join(map(str, digits(k, 4)[1:])); return "01" in s or "10" in s
%o def ok(n): return has01or10(n) and not has01or10(n+1)
%o print(list(filter(ok, range(613)))) # _Michael S. Branicky_, Apr 20 2021
%Y Cf. A007090, A044446.
%K nonn,base
%O 1,1
%A _Clark Kimberling_
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