OFFSET
1,1
COMMENTS
The number of prime divisors is at least 3, because p + q is even and not twice a prime.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(2) = 4073 is a term because 4073, 4079, 4091 are consecutive primes with
4073 + 4079 = 8152 = 2^3 * 1019,
4073 + 4091 = 8164 = 2^2 * 13 * 157,
4079 + 4091 = 8170 = 2 * 5 * 19 * 43, and
4073 + 4079 + 4091 = 12243 = 3 * 7 * 11 * 53
all have 4 prime divisors, counted with multiplicity.
MAPLE
R:= NULL: count:= 0:
p:= 2: q:= 3: r:= 5: v:= numtheory:-bigomega(q+r);
while count < 100 do
p:= q; q:= r; r:= nextprime(r);
w:= numtheory:-bigomega(q+r);
if w = v and numtheory:-bigomega(p+r) = v and numtheory:-bigomega(p+q+r) = v then
R:= R, p; count:= count+1;
fi;
v:= w;
od:
R;
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Jan 05 2024
STATUS
approved