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Numbers k such that string 1,0 occurs in the base-4 representation of k but not of k+1.
2

%I #16 Apr 20 2021 16:15:33

%S 4,20,36,52,84,100,116,132,148,164,180,196,212,228,244,340,356,372,

%T 388,404,420,436,452,468,484,500,516,532,548,564,596,612,628,644,660,

%U 676,692,708,724,740,756,772,788,804,820,852,868,884,900,916,932,948,964

%N Numbers k such that string 1,0 occurs in the base-4 representation of k but not of k+1.

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o def has10(k): s = "".join(map(str, digits(k, 4)[1:])); return "10" in s

%o def ok(n): return has10(n) and not has10(n+1)

%o print(list(filter(ok, range(965)))) # _Michael S. Branicky_, Apr 20 2021

%Y Cf. A007090, A097357, A085805, A043880.

%K nonn,base

%O 1,1

%A _Clark Kimberling_

%E a(5) = 68 removed by _Georg Fischer_, Jun 27 2019