A277623 Each odd term "t" of the sequence is followed by t even terms and each odd digit "k" of the sequence is followed by k even digits.

1, 2, 3, 4, 6, 8, 5, 20, 22, 210, 10, 12, 7, 24, 26, 28, 212, 14, 16, 18, 9, 40, 42, 44, 46, 214, 30, 48, 32, 60, 101, 216, 34, 62, 36, 64, 38, 66, 50, 68, 80, 52, 82, 84, 54, 86, 88, 56, 200, 218, 58, 202, 230, 2010, 70, 204, 206, 72, 208, 220, 74, 222, 224, 76, 226, 228, 78, 240, 242, 90, 244, 246, 2012, 92, 248

Offset

1,2

Comments

After a(1) = 1, the sequence is always extended with the smallest integer not yet present which does not lead to a contradiction.

In a private mail to Eric Angelini, Lars Blomberg wrote about the b-file: "Only the odd terms 1, 3, 5, 7, 9, 101, 103, 21, 201 and 2000001 [are in the b-file]; so the sequence will continue with 2000001 even numbers and odd one."

The sequence could be started with the even term a(0) = 0, which would not impose any restriction and thus be followed by the next smallest possible integer, a(1) = 1. The sequence is not a permutation of the positive integers because some numbers (11, 13, 15, 17, 19, 31, ..., 97, 99, 100, 102,..., 110, 111, ..., 119, 130, ...) = A277694 can never occur. (The odd digit 1 must be followed by 1 even digit, etc.) The previous comment shows why odd terms occur late, but probably (I conjecture) any odd term which is not excluded a priori will occur sooner or later. - M. F. Hasler, Oct 27 2016

Links

Lars Blomberg, Table of n, a(n) for n = 1..461

Example

There are respectively 1 even term after "1" (this is "2"), then 3 even terms after "3" (they are 4, 6 and 8), then 5 even terms after "5" (they are 20, 22, 210, 10 and 12), then 7 even terms after "7" (they are 24, 26, 28, 212, 14, 16 and 18), etc.
But there are also respectively 1 even digit after "1" (this is "2"), then 3 even digits after "3" (they are 4, 6 and 8), then 5 even digits after "5" (they are 2, 0, 2, 2 and 2), then 1 even digit after the "1" of "210" (this is the "0" of "210"), then 1 even digit after the "1" of "10" (this is the "0" of "10"), then 1 even digit after the "1" of "12" (this is the "2" of "12"), then 7 even digits after "7" (they are 2, 4, 2, 6, 2, 8 and 2), etc.

Prog

(PARI) a=u=[c=d=1]; (chk(k, c)=!for(i=1, #k=digits(k), !c==bittest(k[i], 0)||return; c--<0&&c=k[i])); for(n=1, 99, for(k=u[1]+1, 9e9, c&&bittest(k, 0)&&next; setsearch(u, k)&&next; chk(k, d)||next; print1(k", "); a=concat(a, k); u=setunion(u, [k]); c--<0&&c=k; for(i=1, #k=digits(k), d--<0&&d=k[i]); break)); a \\ M. F. Hasler, Oct 27 2016

Crossrefs

Sequence in context: A257690 A336322 A277519 * A082315 A342266 A082320

Adjacent sequences: A277620 A277621 A277622 * A277624 A277625 A277626

Keyword

nonn,base

Author

Eric Angelini and Lars Blomberg, Oct 24 2016

Status

approved