A292575 - OEIS

%I #59 Nov 27 2017 11:37:18

%S 1,2,3,5,4,8,7,9,7,12,13,15,11,16,17,16,14,19,21,25,20,28,27,26,24,27,

%T 31,33,28,33,32,30,31,33,35,40,35,46,44,45,41,48,53,55,47,53,54,50,51,

%U 51,53,58,55,64,60,61,59,61,66,65,60,62,63,61,63,64,63,68,66,75,73,75,70,81,86,90,79,89,91,86,85,89

%N For 1 <= n <= 3, a(n) = n; thereafter, a(2n) = a(n) + a(n+1), a(2n-1) = a(n) + a(n-2).

%C The fractal nature of the sequence is emphasized in the scatterplot of a(n) - n (see Links section). - _Rémy Sigrist_, Nov 26 2017

%H Rémy Sigrist, <a href="/A292575/b292575.txt">Table of n, a(n) for n = 1..25000</a>

%H Rémy Sigrist, <a href="/A292575/a292575.png">Scatterplot of (n, a(n)-n) for n=1..25000</a>

%e For a(4)..a(19) we have that: 2+3=5, 1+3=4, 3+5=8, 2+5=7, 5+4=9, 3+4=7, 4+8=12, 5+8=13, 8+7=15, 4+7=11, 7+9=16, 8+9=17, 9+7=16, 7+7=14, 7+12=19, 9+12=21.

%t Fold[Append[#1, If[EvenQ[#2], #1[[#2]] + #1[[#2 + 1]] & @@ {#1, #2/2}, #1[[#2]] + #1[[#2 - 2]] & @@ {#1, (#2 + 1)/2}]] &, Range@ 3, Range[4, 82]] (* _Michael De Vlieger_, Nov 26 2017 *)

%Y Cf. A000045.

%K nonn

%O 1,2

%A _Martin Michael Musatov_, Oct 02 2017

%E Better definition, corrected and extended by _Omar E. Pol_, Oct 03 2017