cp's OEIS Frontend

A351565 Odd part of Kimberling's paraphrases: a(n) = A000265(A003602(n)).

%I A351565 #14 Jan 03 2024 23:47:40
%S A351565 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 A351565 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 A351565 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 A351565 Odd part of Kimberling's paraphrases: a(n) = A000265(A003602(n)).
%H A351565 Antti Karttunen, <a href="/A351565/b351565.txt">Table of n, a(n) for n = 1..16384</a>
%H A351565 Antti Karttunen, <a href="/A351565/a351565.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A351565 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A351565 a(n) = A000265(A003602(n)) = A000265(1+A000265(n)).
%o A351565 (PARI)
%o A351565 A000265(n) = (n>>valuation(n,2));
%o A351565 A351565(n) = A000265(1+A000265(n));
%o A351565 (Python)
%o A351565 def A351565(n): return (m:=1+(n>>(~n&n-1).bit_length()))>>(~m&m-1).bit_length()  # _Chai Wah Wu_, Jan 03 2024
%Y A351565 Cf. A000265, A003602, A023758 (gives the positions of 1's after its initial zero-term).
%Y A351565 Cf. also A336698, A336699.
%K A351565 nonn
%O A351565 1,5
%A A351565 _Antti Karttunen_, Mar 27 2022