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

1,2

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, ...

Links

Table of n, a(n) for n=1..36.

Example

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.

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]);

Crossrefs

Cf. A001222, A078843, A376481.

Sequence in context: A165298 A352507 A117148 * A343272 A305595 A320687

Adjacent sequences: A376477 A376478 A376479 * A376481 A376482 A376483

Keyword

nonn

Author

Robert Israel, Sep 24 2024

Status

approved