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A368785
Least of three consecutive primes p, q, r such that p + q, p + r, q + r and p + q + r all have the same number of prime divisors, counted with multiplicity.
2
1559, 4073, 5237, 5987, 12119, 14633, 24697, 29881, 29947, 30113, 32003, 41903, 45863, 60169, 64817, 67601, 69151, 71263, 73783, 77713, 78929, 79633, 86629, 88547, 91493, 95483, 96181, 108037, 109859, 110459, 111667, 125471, 132833, 133283, 140419, 142049, 160001, 165133, 170579, 171803, 171827, 171947
OFFSET
1,1
COMMENTS
The number of prime divisors is at least 3, because p + q is even and not twice a prime.
LINKS
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
Sequence in context: A186393 A025026 A362203 * A368786 A343867 A302057
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Jan 05 2024
STATUS
approved