%I #8 Nov 18 2021 00:07:03
%S 95,6,15,39,14,22,119,87,57,46,123,215,159,94,93,219,74,118,122,303,
%T 142,134,327,166,695,178,395,206,214,226,447,959,262,254,543,291,302,
%U 326,334,699,346,358,382,386,394,843,1727,879,446,454,478,482,502,8159,514
%N a(n) = A347113(A347313(n))+1.
%C These numbers generate primes in A347113.
%C Let s = A347113, j = s(i)+1, and k = s(i+1). For prime k, j is a squarefree semiprime pq, p < q.
%C The first 3 primes in s have k = p, while all others observed for i <= 2^19 have k = q.
%H Michael De Vlieger, <a href="/A349405/b349405.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael De Vlieger, <a href="/A349405/a349405.txt">Extended table of n, a(n) for n = 1..23082</a> (all terms resulting from 2^19 terms of A347113)
%H Michael De Vlieger, <a href="/A349405/a349405.png">Log-log scatterplot of A347113(n)</a> n=1..256, indicating primes in green, labeling them with the value a(n) = A347113(n-1)+1. Red dots represent records A347307 in A347113, and blue represent local minima A347756 in A347113.
%e a(1) = s(6)+1 = 95 -> s(7) = 5,
%e a(2) = s(7)+1 = 6 -> s(8) = 2,
%e a(3) = s(10)+1 = 15, -> s(11) = 3,
%e a(4) = s(18)+1 = 39, -> s(19) = 13, etc.
%t c[_] = 0; j = m = 2; m = {1}~Join~Reap[Do[If[IntegerQ@ Log2[i], While[c[m] > 0, m++]]; Set[k, m]; While[Or[c[k] > 0, k == j, GCD[j, k] == 1], k++]; Sow[k]; Set[c[k], i]; j = k + 1, {i, 530}]][[-1, -1]]; m[[Position[m, _?PrimeQ][[All, 1]] - 1]] + 1
%Y Cf. A006530, A020639, A347113, A347313, A348779, A349406.
%K nonn
%O 1,1
%A _Michael De Vlieger_, Nov 16 2021