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

2, 3, 5, 13, 7, 53, 107, 181, 11, 23, 59, 151, 29, 19, 233, 31, 61, 197, 17, 199, 41, 193, 97, 109, 37, 281, 47, 71, 131, 79, 149, 103, 241, 137, 191, 239, 113, 163, 43, 653, 617, 853, 673, 89, 937, 67, 571, 599, 751, 83, 101, 1103, 829, 457, 499, 229

Offset: 1

Author

N. J. A. Sloane, Oct 30 2005

Keywords

• nonn

Comments

Smallest missing prime in A109890 for n <= 10^5 is prime(1821) = 15619. - Michael De Vlieger, Apr 27 2024

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..113

Crossrefs

Cf. A109890, A111238, A111240.

Programs

Mathematica

nn = 2^14; c[_] := False;
Array[Set[{a[#], c[#]}, {#, True}] &, 2];
s = a[1] + a[2]; v = NextPrime[a[2]];
t = Join[{{2, 2}},
  Reap[Monitor[Do[k = SelectFirst[Divisors[s], ! c[#] &];
  c[k] = True; s += k;
  If[PrimeQ[k], Sow[{k, n}];
    If[k == v, While[c[v], v = NextPrime[v]]]], {n, 3, nn}], n] ][[-1, 1]] ];
TakeWhile[t, First[#] <= v &][[All, 1]] (* Michael De Vlieger, Apr 27 2024 *)