This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A327036 #18 Jan 10 2021 11:02:43 %S A327036 0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,12,13,13,14,15,15,16, %T A327036 17,17,18,19,19,21,22,24,24,25,26,26,27,28,28,29,30,30,31,32,33,36,36, %U A327036 37,38,38,39,40,40,41,43,44,47,47,48,49,49,51,51,54,55,58,58,59,60,60 %N A327036 a(0)=0; for n > 0, a(n) is the number of distinct digit strings that occur at least twice (not counting overlapping occurrences) in the concatenation of all previous terms. %C A327036 To calculate a(n) take all the terms from a(0) to a(n-1), concatenate them, and then count the distinct digit strings that have at least two nonoverlapping occurrences. For example, if the concatenated terms formed the string '2210102240404' then the next term would be 8 as the strings '0','1','2','4','04','10','22','40' have all occurred at least twice. Note that the string '404' is not counted as its two occurrences overlap. %C A327036 In the first 20000 terms, the largest increase in consecutive terms is from a(16496) = 45375 to a(16497) = 45410, an increase of 35; the concatenation of a(16496) to the previous terms results in the longest repeated string, '245352453624537'. %e A327036 a(1) = 0 as there have been no repeated strings prior to a(1). %e A327036 a(2) = 1 as there has been one repeat of '0', which occurs in a(0) and a(1). %e A327036 a(3) = 1 as only '0' has repeated up to a(2). %e A327036 a(4) = 2 as now both '0' and '1' have repeated up to a(3). %e A327036 a(22) = 12 as the strings '0' to '10' have repeated, but '10,10' contains the string '01' which also appears from a(1) to a(2), thus '01' has also repeated. %e A327036 a(23) = 13 as a(22) = '12' created a repeat of the string '12', with a(3) and a(4). Even though the terms '10,10,12' contain two occurrences of the string '101' they overlap so are not counted. The string '10,12' also contains another '01' but that has already repeated and been counted previously so is ignored as the count is of distinct strings. %Y A327036 Cf. A225224, A329818, A329448. %Y A327036 Cf. A330015 (same sequence, but overlapping instances of the same digit string are counted among the repeats). %K A327036 nonn,base %O A327036 0,5 %A A327036 _Scott R. Shannon_, Nov 28 2019