cp's OEIS Frontend

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.

%I A365704 #15 Sep 25 2023 08:47:48
%S A365704 10,1000,11,1001,1002,1003,12,13,14,1004,1005,15,16,1006,1007,20,17,
%T A365704 1008,1009,30,18,21,19,31,100,40,101,1010,1011,41,102,1012,1013,50,
%U A365704 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
%N 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.
%C A365704 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;
%C A365704 For a 3-digit integer abc, the "center" is the digit b; the digit immediately to the left of the center is thus a;
%C A365704 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;
%C A365704 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.
%e A365704 The first twelve terms of the sequence are:
%e A365704 10, 1000, 11, 1001, 1002, 1003, 12, 13, 14, 1004, 1005, 15.
%e A365704 We put parentheses around the digit left of center:
%e A365704 (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.
%e A365704 The twelve digits in parentheses are:
%e A365704 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1.
%e A365704 The above twelve digits are the same as the first twelve digits of the sequence:
%e A365704 10, 1000, 11, 1001.
%t A365704 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 *)
%Y A365704 Cf. A365705, A319718.
%K A365704 base,nonn
%O A365704 1,1
%A A365704 _Eric Angelini_, Sep 16 2023
%E A365704 More terms from _Giorgos Kalogeropoulos_, Sep 21 2023