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%I #22 Jan 27 2022 21:22:53
%S 1,111,311,131211,111131111122212,311112132112313114224125115125,
%T 131211212122113133123214124135115135216146227147118128158219159111012101510
%N Similar to the "Look and Say" sequence, with the added requirement that every third digit describes the location of a digit in blocks of three in the previous term.
%C The sequence has a different pattern if, instead of including integers greater than ten in the description of each block of three, one uses symbols to represent those numbers. For example, in a(7), if the subsequence "111012101510" is replaced by "11A12A15A" then the interaction of digits with each other is altered.
%e a(1) is read as "one one in the first block", so a(2) is 111.
%e a(2) is read as "three ones in the first block", so a(3) is 311.
%e a(3) is read as "one three in the first block, two ones in the first block", so a(4) is 131211.
%e a(4) is read as "one one in the first block, one three in the first block, one one in the first block, one two in the second block, two ones in the second block", so a(5) is 111131111122212.
%t {1}~Join~NestList[(s=Split/@Partition[IntegerDigits[#],3];FromDigits@Flatten@Table[Join[Reverse@#,IntegerDigits[k]]&/@({First@#,Length@#}&/@#&/@s)[[k]],{k,Length@s}])&,111,5] (* _Giorgos Kalogeropoulos_, Dec 08 2021 *)
%Y Cf. A005150.
%K nonn,base
%O 1,2
%A _Thomas S. Pedigo_, Dec 06 2021