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A111239 Primes in the order in which they appear in A109890.

%I A111239 #8 Apr 27 2024 12:04:19
%S A111239 2,3,5,13,7,53,107,181,11,23,59,151,29,19,233,31,61,197,17,199,41,193,
%T A111239 97,109,37,281,47,71,131,79,149,103,241,137,191,239,113,163,43,653,
%U A111239 617,853,673,89,937,67,571,599,751,83,101,1103,829,457,499,229
%N A111239 Primes in the order in which they appear in A109890.
%C A111239 Smallest missing prime in A109890 for n <= 10^5 is prime(1821) = 15619. - _Michael De Vlieger_, Apr 27 2024
%H A111239 Michael De Vlieger, <a href="/A111239/b111239.txt">Table of n, a(n) for n = 1..113</a>
%t A111239 nn = 2^14; c[_] := False;
%t A111239 Array[Set[{a[#], c[#]}, {#, True}] &, 2];
%t A111239 s = a[1] + a[2]; v = NextPrime[a[2]];
%t A111239 t = Join[{{2, 2}},
%t A111239   Reap[Monitor[Do[k = SelectFirst[Divisors[s], ! c[#] &];
%t A111239   c[k] = True; s += k;
%t A111239   If[PrimeQ[k], Sow[{k, n}];
%t A111239     If[k == v, While[c[v], v = NextPrime[v]]]], {n, 3, nn}], n] ][[-1, 1]] ];
%t A111239 TakeWhile[t, First[#] <= v &][[All, 1]] (* _Michael De Vlieger_, Apr 27 2024 *)
%Y A111239 Cf. A109890, A111238, A111240.
%K A111239 nonn
%O A111239 1,1
%A A111239 _N. J. A. Sloane_, Oct 30 2005