A365705 Underline the digit immediately to the right of the center of each term (see the Comments section for the definition of "center"). This is the lexicographically earliest sequence of distinct integers > 9 such that the successive underlined digits duplicate the sequence itself, digit by digit.

11, 21, 12, 31, 41, 22, 13, 51, 14, 61, 32, 42, 71, 23, 15, 81, 91, 24, 16, 101, 33, 52, 34, 62, 17, 111, 72, 43, 121, 25, 18, 131, 19, 141, 82, 44, 151, 26, 161, 10, 171, 53, 63, 35, 92, 73, 54, 36, 102, 181, 27, 191, 201, 211, 37, 112, 64, 83, 221, 122, 231, 132, 45, 241, 28, 251, 93

Offset

1,1

Comments

For a 2-digit integer ab, the "center" is the thin space between a and b; the digit immediately to the right of the center is thus b;

For a 3-digit integer abc, the "center" is the digit b; the digit immediately to the right of the center is thus c;

For a 4-digit integer abcd, the "center" is the thin space between b and c; the digit immediately to the left of the center is thus c;

For a 5-digit integer abcde, the "center" is the digit c; the digit immediately to the left of the center is thus d; etc.

Links

Table of n, a(n) for n=1..67.

Example

The first twelve terms of the sequence are:
11, 21, 12, 31, 41, 22, 13, 51, 14, 61, 32, 42.
We put parentheses around the digit right of center:
1(1), 2(1), 1(2), 3(1), 4(1), 2(2), 1(3), 5(1), 1(4), 6(1), 3(2), 4(2).
The twelve digits in parentheses are:
1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 2, 2.
The above twelve digits are the same as the first twelve digits of the sequence:
11, 21, 12, 31, 41, 22.

Mathematica

a[1]=11; a[n_]:=a[n]=(k=10; While[MemberQ[ar=Array[a, n-1], k]||IntegerDigits[k][[Ceiling[IntegerLength@k/2]+1]]!=Flatten[Join[Flatten[IntegerDigits/@ar], IntegerDigits@k]][[n]], k++]; k); Array[a, 70] (* Giorgos Kalogeropoulos, Sep 21 2023 *)

Crossrefs

Cf. A365504, A319718.

Sequence in context: A360470 A125886 A067574 * A299400 A300296 A327246

Adjacent sequences: A365702 A365703 A365704 * A365706 A365707 A365708

Keyword

base,nonn

Author

Eric Angelini, Sep 16 2023

Extensions

More terms from Giorgos Kalogeropoulos, Sep 21 2023

Status

approved