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%I #16 Jun 04 2024 14:24:05
%S 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 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 13,14,15,4,5,6,7,6,7,8,9,7,8,9,10,9,10,11,12,7
%N a(n) is the number of 2s in the binary hereditary representation of 2n.
%C See comments on A266201 for the definition of hereditary representation.
%H Antti Karttunen, <a href="/A361838/b361838.txt">Table of n, a(n) for n = 1..65537</a>
%e A table of n, the binary hereditary representation of 2n, and the number of 2s in the representation:
%e n | hereditary rep. of 2n | number of 2s
%e ---+-------------------------+--------------
%e 1 | 2 | 1
%e 2 | 2^2 | 2
%e 3 | 2^2+2 | 3
%e 4 | 2^(2+1) | 2
%e 5 | 2^(2+1)+2 | 3
%e 6 | 2^(2+1)+2^2 | 4
%e 7 | 2^(2+1)+2^2+2 | 5
%e 8 | 2^2^2 | 3
%e 9 | 2^2^2+2 | 4
%e 10 | 2^2^2+2^2 | 5
%e 11 | 2^2^2+2^2+2 | 6
%e 12 | 2^2^2+2^(2+1) | 5
%e 13 | 2^2^2+2^(2+1)+2 | 6
%e 14 | 2^2^2+2^(2+1)+2^2 | 7
%e 15 | 2^2^2+2^(2+1)+2^2+2 | 8
%e 16 | 2^(2^2+1) | 3
%e 17 | 2^(2^2+1)+2 | 4
%e 18 | 2^(2^2+1)+2^2 | 5
%e 19 | 2^(2^2+1)+2^2+2 | 6
%e 20 | 2^(2^2+1)+2^(2+1) | 5
%e 21 | 2^(2^2+1)+2^(2+1)+2 | 6
%e 22 | 2^(2^2+1)+2^(2+1)+2^2 | 7
%e 23 | 2^(2^2+1)+2^(2+1)+2^2+2 | 8
%e 24 | 2^(2^2+1)+2^2^2 | 6
%e 25 | 2^(2^2+1)+2^2^2+2 | 7
%e 26 | 2^(2^2+1)+2^2^2+2^2 | 8
%e 27 | 2^(2^2+1)+2^2^2+2^2+2 | 9
%e 28 | 2^(2^2+1)+2^2^2+2^(2+1) | 8
%o (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 Cf. A005245, A025280.
%K nonn,base,hear
%O 1,2
%A _Jodi Spitz_, Mar 26 2023