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

1,2

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.

References

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

Links

Table of n, a(n) for n=1..64.

Example

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.

Crossrefs

Cf. A005132, A063733.

Sequence in context: A364467 A357488 A060167 * A118550 A126697 A162406

Adjacent sequences: A234585 A234586 A234587 * A234589 A234590 A234591

Keyword

nonn

Author

Eric Angelini, Dec 31 2013

Extensions

More terms from Jon E. Schoenfield, Jan 11 2014

Status

approved