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 A370577 #13 Feb 25 2024 10:14:59 %S A370577 1,1,2,1,2,2,3,1,2,3,3,4,1,2,3,4,3,4,4,5,1,2,3,4,5,5,6,1,2,3,4,5,6,4, %T A370577 5,6,5,6,6,7,1,2,3,4,5,6,7,7,8,1,2,3,4,5,6,7,8,5,6,7,8,7,8,8,9,1,2,3, %U A370577 4,5,6,7,8,9,7,8,9,9,10,1,2,3,4,5,6,7 %N A370577 Lexicographically earliest sequence such that for any value m, the number of distinct values between a pair of consecutive m's is distinct. %H A370577 Michael S. Branicky, <a href="/A370577/b370577.txt">Table of n, a(n) for n = 1..10000</a> %e A370577 The first terms with the number of distinct values enclosed by m = 1..4 below: %e A370577 n| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 %e A370577 ... %e A370577 a(n)| 1 1 2 1 2 2 3 1 2 3 3 4 1 2 3 4 3 4 4 5 1 2 3 %e A370577 ... %e A370577 ----+--------------------------------------------------------------------- %e A370577 1's| 0, 1, 2, 3, 4, %e A370577 ... %e A370577 2's| 1, 0, 2, 3, 4, %e A370577 ... %e A370577 3's| 2, 0, 3, 1, 4, %e A370577 ... %e A370577 4's| 3, 1, 0, %e A370577 ... %o A370577 (Python) %o A370577 from itertools import islice %o A370577 def agen(): # generator of terms %o A370577 e, a = set(), [] %o A370577 while True: %o A370577 an, allnew = 0, False %o A370577 while not allnew: %o A370577 allnew, an, nd = True, an+1, None %o A370577 for i in range(len(a)-1, -1, -1): %o A370577 if an == a[i]: %o A370577 nd = len(set(a[i+1:])) %o A370577 if (an, nd) in e: allnew = False %o A370577 break %o A370577 yield an; a.append(an); e.add((an, nd)) %o A370577 print(list(islice(agen(), 86))) # _Michael S. Branicky_, Feb 22 2024 %Y A370577 Cf.A330896, A366691, A281511. %K A370577 nonn %O A370577 1,3 %A A370577 _Neal Gersh Tolunsky_, Feb 22 2024 %E A370577 More terms from _Michael S. Branicky_, Feb 22 2024