A253607 First differences of A253580, when the tree is seen as flattened list.

1, -1, 2, 1, -2, -1, 2, 2, 1, -2, -2, -1, 2, 2, 2, 1, -2, -2, -2, -1, 2, 2, 2, 2, 1, -2, -2, -2, -2, -1, 2, 2, 2, 2, 2, 1, -2, -2, -2, -2, -2, -1, 2, 2, 2, 2, 2, 2, 1, -2, -2, -2, -2, -2, -2, -1, 2, 2, 2, 2, 2, 2, 2, 1, -2, -2, -2, -2, -2, -2, -2, -1, 2, 2

Offset: 0

Author

Reinhard Zumkeller, Jan 05 2015

Keywords

• sign

Comments

a(n) != 0 and -2 <= a(n) <= +2.

a(n) = 1 iff A253580(n+1) = A253580(n) + 1, marked with X in the table below, where also the erasure of pairs of consecutive terms in A253580 is illustrated;

a(A005563(n)) = 1; a(A028387(n)) = -1;

a(A061885(n)) > 0; a(A064801(n)) < 0.

Examples

			.   n | A253580(n) | a(n) | erased | reappearing
.  ---+------------+------+--------+-------------
.   0 |    X    0  |   1  |      0 |
.   1 |    X    1  |  -1  |      1 |
.   2 |         0  |   2  |        |           0
.   3 |    X    2  |   1  |      2 |
.   4 |    X    3  |  -2  |      3 |
.   5 |         1  |  -1  |        |           1
.   6 |         0  |   2  |        |           0
.   7 |         2  |   2  |        |           2
.   8 |    X    4  |   1  |      4 |
.   9 |    X    5  |  -2  |      5 |
.  10 |         3  |  -2  |        |           3
.  11 |         1  |  -1  |        |           1
.  12 |         0  |   2  |        |           0
.  13 |         2  |   2  |        |           2
.  14 |         4  |   2  |        |           4
.  15 |    X    6  |   1  |      6 |
.  16 |    X    7  |  -2  |      7 |
.  17 |         5  |  -2  |        |           5
.  18 |         3  |  -2  |        |           3
.  19 |         1  |  -1  |        |           1
.  20 |         0  |   2  |        |           0
.  21 |         2  |   2  |        |           2
.  22 |         4  |   2  |        |           4
.  23 |         6  |   2  |        |           6
.  24 |    X    8  |   1  |      8 |
.  25 |    X    9  |  -2  |      9 |             .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Éric Angelini, More fractal trees - and erasures, SeqFan list, Jan 04 2015.

Crossrefs

Cf. A253580, A005563, A028387, A061885, A064801.

Programs

Haskell

a253607 n = a253607_list !! n
a253607_list = zipWith (-) (tail a253580_list) a253580_list