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 A347619 #11 Sep 11 2021 03:58:05 %S A347619 1,2,3,2,5,3,7,2,5,11,7,3,5,13,17,2,5,11,19,3,5,13,7,11,5,23,29,13,17, %T A347619 31,19,11,23,2,37,41,5,7,37,3,43,47,17,7,23,43,37,31,53,59,29,11,23, %U A347619 61,67,71,73,2,13,79,83,7,13,19,23,89,97,101,103,43,13,107,109,41,79,113,127,3,5 %N A347619 Earliest sequence of integers > 1 such that gcd(a(n),a(n+k)) = 1, where k = 1..a(n-1), with a(1) = 1 and a(2) = 2. %C A347619 As the sequence always takes the earliest number satisfying the restriction gcd(a(n),a(n+k)) = 1, all the terms beyond a(1) will be prime. %e A347619 a(3) = 3, as a(1) = 1, a(2) = 2, so the next one term after a(2) cannot share a divisor with 2, and the smallest such number is 3. %e A347619 a(4) = 2 and a(5) = 5, as a(2) = 2, a(3) = 3, so the next two terms after a(3) cannot share a divisor with 3. The first such term is 2. But now a(3) = 3 and a(4) = 2, so the next three terms after a(4) cannot share a divisor with 2. The smallest number which satisfies both of these restrictions is 5. %Y A347619 Cf. A000040, A027749. %K A347619 nonn %O A347619 1,2 %A A347619 _Scott R. Shannon_, Sep 09 2021