A216603 Indices n for which A216557(n)=0, i.e., n does not reappear as substring in its orbit under A216556.

20, 30, 40, 50, 60, 70, 80, 90, 100, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 155, 156, 157, 158, 159

Offset

1,1

Comments

E. Angelini asked on the SeqFan list whether n=127 is in this sequence. The proof of the affirmative answer was given in the second reply to the post. (But "Lemma 2" should read: There is no n in the range of A216556 such that ...". Indeed, 2016,...,9016 also yield 127 as substring, but are not in A216556.) The same reasoning can be applied to terms 122,...,129.

Links

Table of n, a(n) for n=1..54.

E. Angelini, Strings resurrection, SeqFan mailing list, Sep 08 2012

Example

The number 0 is not in this sequence, because repeated application of A216556 yields 0 > 1 > ... > 9 > 10 which contains 0 as substring, after A216557(0)=10 iterations.
a(1)=20 is the least number which does not occur as a substring in its orbit under A216556. This is the case since no term in (the range of) A216556 may have "20" as a substring.
As explained in A216556 (and obvious from the definition), the digit "0" can only occur preceded by the digit "1". This also explains a(2)=30 through a(9)=100.
In A216557 it is explained why a(10)=111 and all numbers having this or 222,...,999 as substring are in this list.
To see why a(11)=112 and the following terms are in this list, observe that 112 itself has no preimage under A216556 (cf. A216587), and consider all possibilities for "patterns" in which it might occur: Obviously not followed by a digit 0, but possibly by a digit among 1,...,9; and maybe preceded by a digit among 2,...,9. However, all these cases lead to a preimage which has "00" as substring, and is therefore not in the range of A216556.

Crossrefs

Cf. A216556, A216557, A216587, A216589.

Sequence in context: A224400 A132067 A072989 * A166730 A109944 A108030

Adjacent sequences: A216600 A216601 A216602 * A216604 A216605 A216606

Keyword

nonn,base,changed

Author

M. F. Hasler, Sep 09 2012

Status

approved