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Odd part of Kimberling's paraphrases: a(n) = A000265(A003602(n)).
5

%I #14 Jan 03 2024 23:47:40

%S 1,1,1,1,3,1,1,1,5,3,3,1,7,1,1,1,9,5,5,3,11,3,3,1,13,7,7,1,15,1,1,1,

%T 17,9,9,5,19,5,5,3,21,11,11,3,23,3,3,1,25,13,13,7,27,7,7,1,29,15,15,1,

%U 31,1,1,1,33,17,17,9,35,9,9,5,37,19,19,5,39,5,5,3,41,21,21,11,43,11,11,3,45,23,23,3,47

%N Odd part of Kimberling's paraphrases: a(n) = A000265(A003602(n)).

%H Antti Karttunen, <a href="/A351565/b351565.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A351565/a351565.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = A000265(A003602(n)) = A000265(1+A000265(n)).

%o (PARI)

%o A000265(n) = (n>>valuation(n,2));

%o A351565(n) = A000265(1+A000265(n));

%o (Python)

%o def A351565(n): return (m:=1+(n>>(~n&n-1).bit_length()))>>(~m&m-1).bit_length() # _Chai Wah Wu_, Jan 03 2024

%Y Cf. A000265, A003602, A023758 (gives the positions of 1's after its initial zero-term).

%Y Cf. also A336698, A336699.

%K nonn

%O 1,5

%A _Antti Karttunen_, Mar 27 2022