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 A348779 #11 Nov 13 2021 23:37:07
%S A348779 5,2,3,13,7,11,17,29,19,23,41,43,53,47,31,73,37,59,61,101,71,67,109,
%T A348779 83,139,89,79,103,107,113,149,137,131,127,181,97,151,163,167,233,173,
%U A348779 179,191,193,197,281,157,293,223,227,239,241,251,199,257,263,349,269,283,277,401,409,311,421,211,313
%N A348779 Primes in A347113 in order of appearance.
%C A348779 From _Michael De Vlieger_, Nov 13 2021: (Start)
%C A348779 Let s = A347113, j = s(n-1)+1 and k = s(n). Prime k|j = q such that j/q = p, p < q, both primes, in all cases except the first 3, i.e., s(7), s(8), and s(11), with (j, k) = {(95, 5), (6, 2), (15, 3)} respectively.
%C A348779 In other words, squarefree semiprime j = pq, p < q, yields k = q outside of the first 3 primes in s. Are all prime s(n), n > 219 in this category?
%C A348779 Prime k implies k | j, since k = j is not permitted in s, k < j.
%C A348779 There is 1 instance of composite k | j, i.e., s(33) = 25, with j = 75. Are there any others?
%C A348779 The reverse relation j to k is that j is the product of at least one prime divisor p | k and at least one prime q that does not divide k. When k is prime p, j = pq.
%C A348779 Contains local minima in s aside from s(1). A consequence of forbidden j = k in s is that local minima are nonadjacent.
%C A348779 (End)
%H A348779 Michael De Vlieger, <a href="/A348779/b348779.txt">Table of n, a(n) for n = 1..23082</a>
%H A348779 Michael De Vlieger, <a href="/A348779/a348779.png">Log-log scatterplot of A347113(n)</a> for n=1..2^12 showing primes in this sequence in green. Maxima in A347113 appear in red and local minima in blue.
%t A348779 c[_] = 0; m = 1; k = 2; Reap[Monitor[Do[If[IntegerQ@ Log2[i], While[c[k] > 0, k++]]; Set[n, k]; While[Or[c[n] > 0, n == m + 1, GCD[n, m + 1] == 1], n++]; If[PrimeQ[n], Sow[n]]; Set[c[n], i]; m = n, {i, 648}], i]][[-1, -1]] (* _Michael De Vlieger_, Nov 13 2021 *)
%Y A348779 Cf. A347113.
%K A348779 nonn
%O A348779 1,1
%A A348779 _N. J. A. Sloane_, Nov 13 2021