A379045 a(1) = 1. For n > 1, a(n) is the least odd prime p which cannot be represented as the sum of a subset of the previous terms.

1, 3, 5, 7, 17, 19, 53, 67, 173, 211, 439, 997, 1993, 2801, 4969, 6791, 13697, 18661, 50849, 50971, 106669, 152729, 310127, 412333, 826097, 1134841, 2271053, 2991883, 4952809, 7223627, 18574201, 20534933, 40243939, 60778433, 100713031, 222270319, 241670423, 563829493

Offset: 1

Author

Chittaranjan Pardeshi, Dec 14 2024

Keywords

• nonn

Examples

			11 is not a term since 11 = 7 + 3 + 1.
13 is not a term since 13 = 7 + 5 + 1.
		

Crossrefs

Cf. A060341, A225947.

Programs

Maple

b:= proc(n, i) option remember; n=0 or i>0 and s(i)>=n
      and (b(n, i-1) or a(i)<=n and b(n-a(i), i-1))
    end:
s:= proc(n) option remember; `if`(n<1, 0, s(n-1)+a(n)) end:
a:= proc(n) option remember; local p; p:= a(n-1);
      while b(p, n-1) do p:= nextprime(p) od; p
    end: a(1), a(2):=1, 3:
seq(a(n), n=1..26);  # Alois P. Heinz, Dec 15 2024

Mathematica

b[n_, i_] := b[n, i] = n == 0 || i > 0 && s[i] >= n
   && (b[n, i-1] || a[i] <= n && b[n - a[i], i-1]);
s[n_] := s[n] = If[n < 1, 0, s[n-1] + a[n]];
a[n_] := a[n] = Module[{p = a[n-1]},
   While[b[p, n-1], p = NextPrime[p]]; p];
{a[1], a[2]} = {1, 3};
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 02 2025, after Alois P. Heinz *)

Extensions

a(21)-a(37) from Alois P. Heinz, Dec 14 2024

a(38) from Jinyuan Wang, Dec 16 2024