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A361838 a(n) is the number of 2s in the binary hereditary representation of 2n.

%I A361838 #34 Aug 18 2025 19:25:57
%S A361838 1,2,3,2,3,4,5,3,4,5,6,5,6,7,8,3,4,5,6,5,6,7,8,6,7,8,9,8,9,10,11,4,5,
%T A361838 6,7,6,7,8,9,7,8,9,10,9,10,11,12,7,8,9,10,9,10,11,12,10,11,12,13,12,
%U A361838 13,14,15,4,5,6,7,6,7,8,9,7,8,9,10,9,10,11,12,7
%N A361838 a(n) is the number of 2s in the binary hereditary representation of 2n.
%C A361838 See comments on A266201 for the definition of hereditary representation.
%H A361838 Antti Karttunen, <a href="/A361838/b361838.txt">Table of n, a(n) for n = 1..65537</a>
%e A361838 A table of n, the binary hereditary representation of 2n, and the number of 2s in the representation:
%e A361838  n | hereditary rep. of 2n   | number of 2s
%e A361838 ---+-------------------------+--------------
%e A361838  1 | 2                       |      1
%e A361838  2 | 2^2                     |      2
%e A361838  3 | 2^2+2                   |      3
%e A361838  4 | 2^(2+1)                 |      2
%e A361838  5 | 2^(2+1)+2               |      3
%e A361838  6 | 2^(2+1)+2^2             |      4
%e A361838  7 | 2^(2+1)+2^2+2           |      5
%e A361838  8 | 2^2^2                   |      3
%e A361838  9 | 2^2^2+2                 |      4
%e A361838 10 | 2^2^2+2^2               |      5
%e A361838 11 | 2^2^2+2^2+2             |      6
%e A361838 12 | 2^2^2+2^(2+1)           |      5
%e A361838 13 | 2^2^2+2^(2+1)+2         |      6
%e A361838 14 | 2^2^2+2^(2+1)+2^2       |      7
%e A361838 15 | 2^2^2+2^(2+1)+2^2+2     |      8
%e A361838 16 | 2^(2^2+1)               |      3
%e A361838 17 | 2^(2^2+1)+2             |      4
%e A361838 18 | 2^(2^2+1)+2^2           |      5
%e A361838 19 | 2^(2^2+1)+2^2+2         |      6
%e A361838 20 | 2^(2^2+1)+2^(2+1)       |      5
%e A361838 21 | 2^(2^2+1)+2^(2+1)+2     |      6
%e A361838 22 | 2^(2^2+1)+2^(2+1)+2^2   |      7
%e A361838 23 | 2^(2^2+1)+2^(2+1)+2^2+2 |      8
%e A361838 24 | 2^(2^2+1)+2^2^2         |      6
%e A361838 25 | 2^(2^2+1)+2^2^2+2       |      7
%e A361838 26 | 2^(2^2+1)+2^2^2+2^2     |      8
%e A361838 27 | 2^(2^2+1)+2^2^2+2^2+2   |      9
%e A361838 28 | 2^(2^2+1)+2^2^2+2^(2+1) |      8
%o A361838 (PARI) a(n)=if(n==0, 0, sum(k=0, logint(n,2), if(bittest(n,k), 1 + a((k+1)\2)))) \\ _Andrew Howroyd_, Apr 07 2023
%Y A361838 Cf. A005245, A025280.
%K A361838 nonn,base,hear
%O A361838 1,2
%A A361838 _Jodi Spitz_, Mar 26 2023