# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a321211 Showing 1-1 of 1 %I A321211 #20 Sep 03 2024 15:02:30 %S A321211 1,2,3,3,4,4,5,4,6,6,6,7,7,7,8,7,8,9,9,9,9,8,10,9,10,11,11,11,11,12, %T A321211 12,12,11,12,11,12,13,13,13,14,14,14,13,14,14,14,15,14,14,12,14,15,14, %U A321211 15,16,17,17,16,16,16,16,17,16,16,17,17,16,16,15,17,19 %N A321211 Let S be the sequence of integer sets defined by these rules: S(1) = {1}, and for any n > 1, S(n) = {n} U S(pi(n)) U S(n - pi(n)) (where X U Y denotes the union of the sets X and Y and pi is the prime counting function); a(n) = the number of elements of S(n). %C A321211 The prime counting function corresponds to A000720. %C A321211 This sequence has similarities with A294991; a(n) gives approximately the number of intermediate terms to consider in order to compute A316434(n) using the formula of its definition. %H A321211 Rémy Sigrist, Table of n, a(n) for n = 1..10000 %H A321211 Rémy Sigrist, Illustration of a(42) %H A321211 Rémy Sigrist, Density plot of the first 100000000 terms %H A321211 Rémy Sigrist, C++ program for A321211 %e A321211 The first terms, alongside pi(n) and S(n), are: %e A321211 n a(n) pi(n) S(n) %e A321211 -- ---- ----- ---------------------- %e A321211 1 1 0 {1} %e A321211 2 2 1 {1, 2} %e A321211 3 3 2 {1, 2, 3} %e A321211 4 3 2 {1, 2, 4} %e A321211 5 4 3 {1, 2, 3, 5} %e A321211 6 4 3 {1, 2, 3, 6} %e A321211 7 5 4 {1, 2, 3, 4, 7} %e A321211 8 4 4 {1, 2, 4, 8} %e A321211 9 6 4 {1, 2, 3, 4, 5, 9} %e A321211 10 6 4 {1, 2, 3, 4, 6, 10} %e A321211 11 6 5 {1, 2, 3, 5, 6, 11} %e A321211 12 7 5 {1, 2, 3, 4, 5, 7, 12} %o A321211 (C++) // See Links section. %o A321211 (PARI) a(n) = my (v=Set([-1, -n]), i=1); while (v[i]!=-1, my (pi=primepi(-v[i])); v=setunion(v, Set([v[i]+pi, -pi])); i++); #v %Y A321211 Cf. A000720, A294991, A316434. %K A321211 nonn %O A321211 1,2 %A A321211 _Altug Alkan_ and _Rémy Sigrist_, Oct 31 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE