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A380110 In the base 4 expansion of n: map 0->0, 1->1, 2->1, 3->2.

%I A380110 #74 Feb 27 2025 07:57:09
%S A380110 0,1,1,2,4,5,5,6,4,5,5,6,8,9,9,10,16,17,17,18,20,21,21,22,20,21,21,22,
%T A380110 24,25,25,26,16,17,17,18,20,21,21,22,20,21,21,22,24,25,25,26,32,33,33,
%U A380110 34,36,37,37,38,36,37,37,38,40,41,41,42,64,65,65,66,68,69
%N A380110 In the base 4 expansion of n: map 0->0, 1->1, 2->1, 3->2.
%C A380110 This is essentialy the mapping of the half adder where the inputs A,B maps to outputs: C_out and S as in binary: 00->00, 01->01, 10->01, 11->10, where C_out is the carry out bit and S is the sum bit.
%C A380110 The fixed points for this sequence are in the Moser-de Bruijn sequence (A000695).
%H A380110 Paolo Xausa, <a href="/A380110/b380110.txt">Table of n, a(n) for n = 0..10000</a>
%H A380110 Wikipedia, <a href="https://en.wikipedia.org/wiki/Adder_(electronics)">Adder (electronics)</a>
%F A380110 a(n) = n iff n in A000695.
%F A380110 a(2^k) = A213173(n).
%F A380110 a(n) = a(n-1)+1 if n odd.
%F A380110 a(n) = n-A063695(n)/2.
%e A380110 Half adder truth table:
%e A380110  A | B | C_out | S
%e A380110 ---+---+-------+------
%e A380110  0 | 0 | 0     | 0
%e A380110  0 | 1 | 0     | 1
%e A380110  1 | 0 | 0     | 1
%e A380110  1 | 1 | 1     | 0
%e A380110 For n = 25 a(25) = 21 because:
%e A380110 25 = 121_4 and 121_4 maps to 111_4 which is 21.
%t A380110 A380110[n_] := FromDigits[ReplaceAll[IntegerDigits[n, 4], {2 -> 1, 3 -> 2}], 4];
%t A380110 Array[A380110, 100, 0] (* _Paolo Xausa_, Feb 27 2025 *)
%o A380110 (Python)
%o A380110 def a(n):
%o A380110     r,p = 0,1
%o A380110     while n:
%o A380110         ps = (n & 1) + ((n >> 1) & 1)
%o A380110         r += ps * p
%o A380110         n >>= 2
%o A380110         p <<= 2
%o A380110     return r
%o A380110 print([a(n) for n in range(70)])
%Y A380110 Cf. A000079, A000695, A063695, A213173.
%K A380110 nonn,base,easy
%O A380110 0,4
%A A380110 _Darío Clavijo_, Feb 14 2025