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

Author

Eric Angelini, Sep 16 2023

Keywords

• base
• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A365705, A319718.

Programs

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 *)

Extensions

More terms from Giorgos Kalogeropoulos, Sep 21 2023