A376481 a(n) is the first partial sum of the numbers with n prime factors, counted with multiplicity, that is prime.

2, 19, 113, 367, 2161, 9791, 127781, 255019, 1090421, 6031891, 27701213, 124489399, 584289157, 2772603503, 13172647021, 59835586439, 279157058197, 1302096836543, 6106904040253, 28448035817911, 132707231124773, 617761562462063, 2866868448935501, 13305669027668711, 61658859228014773

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..25.

Example

a(3) = 113 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$n]], pq);
s:= 0;
for count from 1 do
 t:= extract(pq);
 v:= -t[1];
 w:= t[2];
 s:= s+v;
 if isprime(s) then return s fi;
 p:= nextprime(w[-1]);
 for i from n to 1 by -1 while w[i] = w[n] do
   insert([t[1]*(p/w[-1])^(n+1-i), [op(w[1..i-1]), p$(n+1-i)]], pq)
 od od;
end proc:
map(f, [$1..36]);

Crossrefs

Cf. A001222, A376480.

Sequence in context: A240124 A278405 A285791 * A101253 A082291 A055518

Adjacent sequences: A376478 A376479 A376480 * A376482 A376483 A376484

Keyword

nonn

Author

Robert Israel, Sep 24 2024

Status

approved