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 A375907 #13 Sep 03 2024 01:06:14 %S A375907 2,4,3,6,2,4,3,6,2,3,6,2,4,8,10,3,6,5,10,2,4,3,6,2,3,6,2,4,8,10,3,6,5, %T A375907 10,2,3,6,2,4,8,10,3,6,5,10,2,4,3,6,2,4,8,10,5,15,2,4,6,3,9,12,8,10,5, %U A375907 15,2,4,6,5,10,2,4,6,3,2,4,6,3,9,2,4,6,3,9,12,8,10,5,15,2,4,3,6,2,4 %N A375907 Lexicographically earliest sequence where a(n) is the length of the n-th block of distinct integers sharing a prime factor. %C A375907 Does every positive integer > 1 appear eventually? %H A375907 Michael S. Branicky, <a href="/A375907/b375907.txt">Table of n, a(n) for n = 1..10000</a> %e A375907 The sequence and blocks begin %e A375907 n = 1 2 3 4 5 6 7 8 9 ... %e A375907 a(n) = 2,4, 3,6,2,4, 3,6,2, 3,6,2,4,8,10, 3,6, ... %e A375907 block \-/ \-----/ \---/ \----------/ \-/ %e A375907 length 2 4 3 6 2 ... %e A375907 a(7) = 3 is the start of a new block since it has no common factor with the preceding a(6) = 4. %e A375907 The block lengths are the sequence itself. %o A375907 (Python) %o A375907 from math import gcd %o A375907 from itertools import count, islice %o A375907 def agen(): # generator of terms %o A375907 n, an, alst = 1, 2, [-3] %o A375907 while True: %o A375907 b = [next(i for i in count(2) if gcd(i, alst[-1])==1)] %o A375907 for i in range(an-1): %o A375907 b += [next(j for j in count(2) if j not in b and gcd(j, b[-1])!=1)] %o A375907 yield from b %o A375907 alst.extend(b) %o A375907 n, an = n+1, alst[n+1] %o A375907 print(list(islice(agen(), 95))) # _Michael S. Branicky_, Sep 02 2024 %K A375907 nonn %O A375907 1,1 %A A375907 _Bryle Morga_, Sep 02 2024