A376480 a(n) is the least k such that the sum of the first k numbers with n prime factors, counted with multiplicity, is prime.

1, 3, 6, 8, 15, 24, 68, 68, 103, 179, 280, 432, 681, 1078, 1705, 2630, 4110, 6414, 10029, 15611, 24297, 37746, 58506, 90631, 140203, 216630, 334543, 516159, 795637, 1225649, 1886573, 2901816, 4460387, 6851543, 10518523, 16138688

Offset: 1

Author

Robert Israel, Sep 24 2024

Keywords

• nonn

Comments

For n >=2, a(n) >= A078843(n), as for k < A078843(n) the sum of the first k is even. a(n) = A078843(n) for n = 2, 4, 9, 18, ...

Examples

			a(3) = 6 because the sum of the first 6 triprimes is 8 + 12 + 18 + 20 + 27 + 28 = 113 which is prime, and none of the previous partial sums is prime.
		

Crossrefs

Cf. A001222, A078843, A376481.

Programs

Maple

f:= proc(n)
uses priqueue;
 local pq, t, s, count,v, w, p, i;
 initialize(pq);
 insert([-2^n, [2$n]],pq);
 s:= 0;
 for count from 1 do
   t:= extract(pq);
   v:= -t[1];
   w:= t[2];
   s:= s+v;
   if isprime(s) then return count fi;
   p:= nextprime(w[-1]);
   for i from n to 1 by -1 while w[i] = w[n] do
      insert([t[1]*(p/w[-1])^(n+1-i),[op(w[1..i-1]),p$(n+1-i)]],pq);
 od od;
end proc:
map(f, [$1..36]);