A365705 - OEIS

%I #12 Sep 25 2023 08:48:15

%S 11,21,12,31,41,22,13,51,14,61,32,42,71,23,15,81,91,24,16,101,33,52,

%T 34,62,17,111,72,43,121,25,18,131,19,141,82,44,151,26,161,10,171,53,

%U 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 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 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 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 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 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 The first twelve terms of the sequence are:

%e 11, 21, 12, 31, 41, 22, 13, 51, 14, 61, 32, 42.

%e We put parentheses around the digit right of center:

%e 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 The twelve digits in parentheses are:

%e 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 2, 2.

%e The above twelve digits are the same as the first twelve digits of the sequence:

%e 11, 21, 12, 31, 41, 22.

%t 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 Cf. A365504, A319718.

%K base,nonn

%O 1,1

%A _Eric Angelini_, Sep 16 2023

%E More terms from _Giorgos Kalogeropoulos_, Sep 21 2023