A112377 A self-descriptive fractal sequence: if 1 is subtracted from every term and any zero terms are omitted, the original sequence is recovered (this process may be called "lower trimming").

1, 2, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 5, 1, 2, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 6, 1, 2, 1, 1, 3, 1, 2, 1, 2, 1

Offset

0,2

Comments

This sequence is also self-descriptive, in that each element gives the number of zeros that were removed before it. The indices where the sequence hits a new maximum value (2 at the 2nd position, 3 at the 5th position, 4 at the 13th, 5 at the 34th, etc.) are every second Fibonacci number.

Links

Table of n, a(n) for n=0..98.

Mathematica

lowertrim[list_] := DeleteCases[list - 1, 0];
Nest[Flatten[Append[#, {ConstantArray[1, #[[Length[lowertrim[#]] + 1]]], #[[Length[lowertrim[#]] + 1]] + 1}]] &, {1, 2}, 15] (* Birkas Gyorgy, Apr 27 2011 *)

Crossrefs

Cf. A112378, A112379, A112380, A000045, A112382.

Sequence in context: A107359 A307641 A342255 * A354521 A277760 A371572

Adjacent sequences: A112374 A112375 A112376 * A112378 A112379 A112380

Keyword

nonn,easy,nice

Author

Kerry Mitchell, Dec 04 2005

Status

approved