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A376503
Primes p such that p + 2, p + 4 and p + 6 are products of 3, 5 and 7 primes respectively (counted with multiplicity)
1
171869, 5609369, 7653119, 11177069, 11320709, 11479319, 12325619, 13530119, 15426419, 15558119, 17136619, 17541869, 17851919, 18809369, 18843119, 19593869, 19634369, 19938119, 20806619, 21600419, 22470953, 23637839, 23796869, 23999369, 24006119, 24275819, 25798739, 25879001, 25965869, 26278169
OFFSET
1,1
COMMENTS
Since 2 and 3 are not terms, the least possible prime factor of p + 6 is 5. This is why, at least initially, it seems most terms end in 9.
LINKS
EXAMPLE
a(3) = 7653119 is a term because 7653119 is prime,
7653121 = 7 * 61 * 17923 has 3 prime factors,
7653123 = 3^4 * 94483 has 5 prime factors, and
7653125 = 5^5 * 31 * 79 has 7 prime factors, counted with multiplicity.
MAPLE
with(priqueue):
R:= NULL: count:= 0:
initialize(pq):
insert([-5^7, [5$7]], pq):
for iter from 1 while count < 100 do
t:= extract(pq);
v:= -t[1]; w:= t[2];
if isprime(v-6) and numtheory:-bigomega(v-4) = 3 and numtheory:-bigomega(v-2) = 5 then
R:= R, v-6; count:= count+1;
fi;
p:= nextprime(w[-1]);
for i from 7 to 1 by -1 while w[i] = w[7] do
insert([t[1]*(p/w[7])^(8-i), [op(w[1..i-1]), p$(8-i)]], pq);
od;
od:
R;
CROSSREFS
Sequence in context: A246227 A206115 A204730 * A049053 A242980 A221742
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Sep 25 2024
STATUS
approved