A043880 Numbers k such that 0 and 1 occur juxtaposed in the base-4 representation of k but not of k+1.

4, 20, 33, 36, 49, 52, 84, 97, 100, 113, 116, 129, 135, 148, 161, 164, 177, 180, 193, 199, 212, 225, 228, 241, 244, 340, 353, 356, 369, 372, 385, 391, 404, 417, 420, 433, 436, 449, 455, 468, 481, 484, 497, 500, 513, 519, 543, 545, 548, 561, 564, 596, 609, 612

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Crossrefs

Cf. A007090, A044446.

Programs

Mathematica

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 *)

Python

from sympy.ntheory.factor_ import digits
def has01or10(k):
  s = "".join(map(str, digits(k, 4)[1:])); return "01" in s or "10" in s
def ok(n): return has01or10(n) and not has01or10(n+1)
print(list(filter(ok, range(613)))) # Michael S. Branicky, Apr 20 2021