A330599 If a(n) uses fewer digits than a(n+1), we compute K = |a(n) - a(n+1)|. The successive such Ks rebuild the sequence itself, with a(1) = 5.

5, 10, 1, 11, 99, 100, 2, 13, 112, 3, 103, 998, 1000, 4, 17, 129, 9, 12, 115, 1113, 6, 1006, 97, 101, 7, 24, 153, 93, 102, 8, 20, 135, 1248, 98, 104, 1110, 14, 111, 15, 116, 994, 1001, 81, 105, 16, 169, 21, 114, 18, 120, 995, 1003, 86, 106, 19, 154, 1402, 23, 121, 22, 126, 1236, 94, 108, 25, 136, 92, 107, 26

Offset

1,1

Comments

The intent of the authors was not to produce the lexicographically earliest sequence S of distinct terms > 0 with this property; instead they used two rules:

Let x be the current last term, y the next term, z the term after that and w a previous term to be matched. The number of digits in x is denoted $x$.

The two rules are:

1) If possible, y is selected so that y - x = w and $y$ > $x$, for example x=5, y=10, w=5 in (5, 10);

2) Otherwise first select y with $y$ <= $x$ and then z so that z - y = w and $z$ > $y$, for example x=10, y=1, z=11, w=10 in (5, 10, 1, 11).

(See the end of the Example section for more.)

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000

Example

As 5 uses fewer digits than 10, we compute K1 = |5-10| = 5;
as 10 uses more digits than 1, we don't do anything;
as 1 uses fewer digits than 11, we compute K2 = |1-11| = 10;
as 11 and 99 use the same number of digits, we don't do anything;
as 99 uses fewer digits than 100, we compute K3 = |99-100| = 1;
as 100 uses more digits than 2, we don't do anything;
as 2 uses fewer digits than 13, we compute K4 = |2-13| = 11;
as 13 uses fewer digits than 112, we compute K5 = |13-112| = 99; etc.
We see that the succession of K1, K2, K3, K4, K5, ... reproduces S.
a(4) = 11 illustrates the Comments section, as a(4) = 2 could also extend S with no contradiction. But 11, one digit longer than 2, was chosen instead.
a(9) = 112 illustrates the same option, as a(9) = 4 could also extend S with no contradiction. But 112, one digit longer than 13, was preferred.

Crossrefs

Sequence in context: A357280 A370131 A258150 * A099731 A307716 A091306

Adjacent sequences: A330596 A330597 A330598 * A330600 A330601 A330602

Keyword

base,nonn

Author

Eric Angelini and Lars Blomberg, Dec 19 2019

Status

approved