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 A340716 #11 Jan 22 2021 14:17:29 %S A340716 1,2,2,3,2,3,4,2,3,5,4,2,3,5,6,4,2,7,3,5,6,4,8,2,7,9,3,5,6,4,10,8,2,7, %T A340716 9,3,5,11,6,4,12,10,8,2,7,9,3,13,5,11,6,4,14,12,10,15,8,2,7,9,16,3,13, %U A340716 5,11,6,4,17,14,12,10,15,8,2,18,7,9,19,16,3 %N A340716 Lexicographically earliest sequence of positive integers with as many distinct values as possible such that for any n > 0, a(n + pi(n)) = a(n) (where pi(n) = A000720(n) corresponds to the number of prime numbers <= n). %C A340716 The condition "with as many distinct values as possible" means here that for any distinct m and n, provided the orbits of m and n under the map x -> x + pi(x) do not merge, then a(m) <> a(n). %C A340716 This sequence has similarities with A003602 (A003602(2*n) = A003602(n)) and with A163491 (A163491(n+ceiling(n/2)) = A163491(n)). %H A340716 Rémy Sigrist, <a href="/A340716/b340716.txt">Table of n, a(n) for n = 1..10000</a> %F A340716 a(n) = 2 iff n belongs to A061535. %F A340716 a(A095116(n)) = n + 1. %e A340716 The first terms, alongside n + pi(n), are: %e A340716 n a(n) n + pi(n) %e A340716 -- ---- --------- %e A340716 1 1 1 %e A340716 2 2 3 %e A340716 3 2 5 %e A340716 4 3 6 %e A340716 5 2 8 %e A340716 6 3 9 %e A340716 7 4 11 %e A340716 8 2 12 %e A340716 9 3 13 %e A340716 10 5 14 %e A340716 11 4 16 %e A340716 12 2 17 %o A340716 (PARI) u=0; for (n=1, #a=vector(80), if (a[n]==0, a[n]=u++); print1 (a[n]", "); m=n+primepi(n); if (m<=#a, a[m]=a[n])) %Y A340716 See A003602, A163491 and A340717 for similar sequences. %Y A340716 Cf. A000720, A095117. %K A340716 nonn,look %O A340716 1,2 %A A340716 _Rémy Sigrist_, Jan 17 2021