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
Robert Israel, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Sep 25 2024
STATUS
approved