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