A234588 Lexicographically earliest sequence S with property that a(n) is the a(n)-th absolute first difference of S.

1, 2, 4, 5, 9, 14, 8, 10, 18, 27, 17, 6, 11, 15, 29, 44, 19, 36, 54, 35, 21, 42, 23, 46, 25, 50, 28, 55, 83, 112, 31, 62, 33, 66, 37, 72, 108, 71, 39, 78, 41, 82, 124, 45, 89, 134, 88, 48, 96, 51, 101, 152, 53, 106, 160, 105, 57, 114, 59, 118, 61, 122, 184, 64

Offset: 1

Author

Eric Angelini, Dec 31 2013

Keywords

• nonn

Comments

A kind of self-describing sequence.

Recamán's sequence A005132 is also self-describing in this sense, but comes lexicographically after this one (and you have to drop the initial "0").

If we want S to be monotonically increasing, we get A063733.

Examples

			If n = 1 2 3 4 5  6 7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 ...
a(n) = 1 2 4 5 9 14 8 10 18 27 17, 6 11 15 29 44 19 36 54 35 21 42 23 46 25 50 28 55 ...
diff =  1 2 1 4 5  6 2  8  9  10 11 5  4  14 15 25 17 18 19 14 21 19 23 21 25 22
d-rank= 1 2 3 4 5  6 7  8  9  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
hit:    * *   * *  *    *  *   *  *     *  *  *     *
S is tricky to compute; the rule for a(n+1) is "always use the smallest integer not yet in S and not leading to a contradiction".
'14' is in S and '14' says: "The 14th absolute first difference in S equals 14" -- which is true.
		

References

• Eric Angelini, Posting to Sequence Fans Mailing List, Nov 26, 2010

Crossrefs

Cf. A005132, A063733.

Extensions

More terms from Jon E. Schoenfield, Jan 11 2014