A292575 For 1 <= n <= 3, a(n) = n; thereafter, a(2n) = a(n) + a(n+1), a(2n-1) = a(n) + a(n-2).

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

Offset

1,2

Comments

The fractal nature of the sequence is emphasized in the scatterplot of a(n) - n (see Links section). - Rémy Sigrist, Nov 26 2017

Links

Rémy Sigrist, Table of n, a(n) for n = 1..25000

Rémy Sigrist, Scatterplot of (n, a(n)-n) for n=1..25000

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A000045.

Sequence in context: A254103 A048673 A288119 * A096070 A075157 A183080

Adjacent sequences: A292572 A292573 A292574 * A292576 A292577 A292578

Keyword

nonn

Author

Martin Michael Musatov, Oct 02 2017

Extensions

Better definition, corrected and extended by Omar E. Pol, Oct 03 2017

Status

approved