cp's OEIS Frontend

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.

%I A365705 #12 Sep 25 2023 08:48:15
%S A365705 11,21,12,31,41,22,13,51,14,61,32,42,71,23,15,81,91,24,16,101,33,52,
%T A365705 34,62,17,111,72,43,121,25,18,131,19,141,82,44,151,26,161,10,171,53,
%U A365705 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
%N 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.
%C A365705 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;
%C A365705 For a 3-digit integer abc, the "center" is the digit b; the digit immediately to the right of the center is thus c;
%C A365705 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;
%C A365705 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.
%e A365705 The first twelve terms of the sequence are:
%e A365705 11, 21, 12, 31, 41, 22, 13, 51, 14, 61, 32, 42.
%e A365705 We put parentheses around the digit right of center:
%e A365705 1(1), 2(1), 1(2), 3(1), 4(1), 2(2), 1(3), 5(1), 1(4), 6(1), 3(2), 4(2).
%e A365705 The twelve digits in parentheses are:
%e A365705 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 2, 2.
%e A365705 The above twelve digits are the same as the first twelve digits of the sequence:
%e A365705 11, 21, 12, 31, 41, 22.
%t A365705 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 *)
%Y A365705 Cf. A365504, A319718.
%K A365705 base,nonn
%O A365705 1,1
%A A365705 _Eric Angelini_, Sep 16 2023
%E A365705 More terms from _Giorgos Kalogeropoulos_, Sep 21 2023