cp's OEIS Frontend

A110962 Fractalization of A025480, zero-based version of Kimberling's paraphrases sequence.

%I A110962 #32 Jul 07 2024 21:15:59
%S A110962 0,0,0,0,1,0,0,0,2,1,1,0,3,0,0,0,4,2,2,1,5,1,1,0,6,3,3,0,7,0,0,0,8,4,
%T A110962 4,2,9,2,2,1,10,5,5,1,11,1,1,0,12,6,6,3,13,3,3,0,14,7,7,0,15,0,0,0,16,
%U A110962 8,8,4,17,4,4,2,18,9,9,2,19,2,2,1,20,10,10,5,21,5,5,1,22,11,11,1,23,1,1,0,24,12,12
%N A110962 Fractalization of A025480, zero-based version of Kimberling's paraphrases sequence.
%C A110962 Self-descriptive sequence: the terms at odd indices are the sequence itself, while the terms at even indices (the skeleton of this sequence) are the terms of A025480, which is a zero-based sequence of Kimberling's paraphrases sequence, A003602.
%H A110962 Antti Karttunen, <a href="/A110962/b110962.txt">Table of n, a(n) for n = 0..65537</a>
%H A110962 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/fractals.html">Fractal sequences</a>
%H A110962 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A110962 For even n, a(n) = A025480(n/2), for odd n, a(n) = a((n-1)/2). - _Antti Karttunen_, Apr 18 2022
%F A110962 a(2n+1) = a(4n+3) = a(n).
%F A110962 a(2n) = a(4n+1) = a(4n+2) = A025480(n/2).
%F A110962 a(4n) = a(8n+1) = a(8n+2) = n.
%F A110962 a(n) = A110963(1+n) - 1.
%o A110962 (PARI)
%o A110962 A025480(n) = (n>>valuation(n*2+2, 2));
%o A110962 A110962(n) = if(!(n%2), A025480(n/2), A110962((n-1)/2)); \\ _Antti Karttunen_, Apr 18 2022
%o A110962 (PARI) a(n) = n++; n>>=valuation(n, 2); n>>valuation(2*n+2, 2); \\ _Ruud H.G. van Tol_, Jun 23 2024
%Y A110962 Cf. A000265, A003602, A025480, A089309, A103391, A110812, A110779, A110766.
%Y A110962 One less than A110963 (note also the different starting offsets).
%K A110962 base,easy,nonn
%O A110962 0,9
%A A110962 _Alexandre Wajnberg_, Sep 26 2005
%E A110962 Entry edited and more terms added by _Antti Karttunen_, Apr 18 2022