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
Keywords
Examples
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.
Programs
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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]);
Comments