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

1,2

Links

Table of n, a(n) for n=1..38.

Example

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

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 *)

Crossrefs

Cf. A060341, A225947.

Sequence in context: A348438 A331800 A062547 * A125739 A219461 A122853

Adjacent sequences: A379042 A379043 A379044 * A379046 A379047 A379048

Keyword

nonn,changed

Author

Chittaranjan Pardeshi, Dec 14 2024

Extensions

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

a(38) from Jinyuan Wang, Dec 16 2024

Status

approved