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A044072 Numbers k such that string 2,3 occurs in the base 4 representation of k but not of k-1. 3

%I #16 Nov 27 2021 04:52:20

%S 11,27,43,59,75,91,107,123,139,155,171,203,219,235,251,267,283,299,

%T 315,331,347,363,379,395,411,427,459,475,491,507,523,539,555,571,587,

%U 603,619,635,651,667,683,779,795,811,827,843,859,875,891,907,923,939,971

%N Numbers k such that string 2,3 occurs in the base 4 representation of k but not of k-1.

%C Members are of form 16k+11, but not all such numbers are in the sequence. The first missing number is 187.

%H Michael S. Branicky, <a href="/A044072/b044072.txt">Table of n, a(n) for n = 1..10000</a>

%t Flatten[Position[Partition[Table[If[MemberQ[Partition[IntegerDigits[n, 4], 2, 1], {2, 3}], 1, 0], {n, 1000}], 2, 1], {0, 1}]] + 1 (* _Vincenzo Librandi_, Aug 19 2015 *)

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o def has23(n): return "23" in "".join(map(str, digits(n, 4)[1:]))

%o def ok(n): return has23(n) and not has23(n-1)

%o print([k for k in range(972) if ok(k)]) # _Michael S. Branicky_, Nov 27 2021

%Y Differs from A106839.

%Y Cf. A044453.

%K nonn,base

%O 1,1

%A _Clark Kimberling_

%E a(48) and beyond from _Michael S. Branicky_, Nov 27 2021

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