A365704 Underline the digit immediately to the left 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.

10, 1000, 11, 1001, 1002, 1003, 12, 13, 14, 1004, 1005, 15, 16, 1006, 1007, 20, 17, 1008, 1009, 30, 18, 21, 19, 31, 100, 40, 101, 1010, 1011, 41, 102, 1012, 1013, 50, 103, 51, 104, 60, 105, 1014, 1015, 61, 106, 1016, 1017, 70, 22, 1018, 107, 71, 108, 1019, 1020, 80, 109, 1021, 1022, 90, 32, 1023, 110, 81, 23

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 left of the center is thus a;

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

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 b;

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

Links

Table of n, a(n) for n=1..63.

Example

The first twelve terms of the sequence are:
10, 1000, 11, 1001, 1002, 1003, 12, 13, 14, 1004, 1005, 15.
We put parentheses around the digit left of center:
(1)0, 1(0)00, (1)1, 1(0)01, 1(0)02, 1(0)03, (1)2, (1)3, (1)4, 1(0)04, 1(0)05, (1)5.
The twelve digits in parentheses are:
1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1.
The above twelve digits are the same as the first twelve digits of the sequence:
10, 1000, 11, 1001.

Mathematica

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

Crossrefs

Cf. A365705, A319718.

Sequence in context: A163566 A168520 A200993 * A062033 A171500 A154027

Adjacent sequences: A365701 A365702 A365703 * A365705 A365706 A365707

Keyword

base,nonn

Author

Eric Angelini, Sep 16 2023

Extensions

More terms from Giorgos Kalogeropoulos, Sep 21 2023

Status

approved