Hello Math-Fun, please have a look here, this is math-fun, I guess, though I have a few worries (in yellow color): http://cinquantesignes.blogspot.com/2020/03/substrings-so-far.html This page starts like this: “Describe my substrings so far” Definition: a(n) is the count of substrings a(n+1) so far in the sequence, including a(n+1) itself. S = 1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,11,1,13,1,15,1,17,1,19,1,21,1,22,1,23,1,24,1,25,1,26,1,27,1,28,1,29,1,31,1,32,1,33,1,34,1,35,1,36,1,37,1,38,1,39,1,41,1,42,1,43,1,44,1,45,1,46,1,47,1,48,1,49,1,51,1,52,1,53,1,54,1,55,1,56,1,57,1,58,1,59,1,61,1,62,1,63,1,64,1,65,1,66,1,67,1,68,1,69,1,71,1,72,1,73,1,74,1,75,1,76,1,77,1,78,1,79,1,81,1,82,1,83,1,84,1,85,1,86,1,87,1,88,1,89,1,91,1,92,1,93,1,94,1,95,1,96,1,97,1,98,1,101,1,103,1,105,1,107,1,109,1,112,1,115,1,118,1,120,1,122,1,124,1,126,1,… S must be “read” like this, term by term from the left to the right: a(1) – there is 1 substring “2” so far in S; (true, if you consider the segment <1,2>); a(2) – there are 2 substrings “1” so far in S; (true, if you consider the segment <1,2,1>); a(3) – there is 1 substring “3” so far in S; (true, if you consider the segment <1,2,1,3>); a(4) – there are 3 substrings “1” so far in S; (true, if you consider the segment <1,2,1,3,1>); a(5) – there is 1 substring “4” so far in S; (true, if you consider the segment <1,2,1,3,1,4>); … a(14) – there are 8 substrings “1” so far in S; (true, if you consider the segment <1,2,1,3,1,4,1,5,1,6,1,7,1,8,1>); a(15) – there is 1 substring “11” so far in S; (true, if you consider the segment <1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,11>); a(16) – there are 11 substrings “1” so far in S; (true, if you consider the segment <1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,11,1>); Etc. Here are my worries: (...)