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A365833
Triprimes a such that, if b is the next triprime, a + b and b - a are also triprimes.
2
130, 195, 222, 292, 498, 582, 670, 814, 970, 1362, 1398, 1534, 1645, 1813, 1834, 1978, 2514, 2717, 2853, 2865, 2994, 3092, 3130, 3157, 3211, 3462, 3897, 4527, 4615, 4707, 4782, 5529, 6070, 6610, 7270, 7399, 7414, 7527, 7767, 8029, 8305, 8687, 8911, 9994, 10330, 10390, 11297, 11557, 11619, 11679
OFFSET
1,1
COMMENTS
It appears that in most cases b - a = 8.
LINKS
EXAMPLE
a(3) = 222 ix a term because 222 = 2*3*37 is a triprime, the next triprime is 230 = 2 5 * 23, and 222 + 230 = 452 = 2^2 * 113 and 230 - 222 = 8 = 2^3 are triprimes.
MAPLE
with(priqueue);
a:= 8: R:= NULL: count:= 0:
initialize(triprimes);
insert([-8, 0, 2], triprimes);
while count < 50 do
v:= extract(triprimes);
if v[2] = 3 then
b:= -v[1];
if numtheory:-bigomega(b-a) = 3 and numtheory:-bigomega(b+a)=3 then
R:= R, a; count:= count+1
fi;
a:= b;
else
insert(v+[0, 1, 0], triprimes);
q:= nextprime(v[3]);
w:= v[1]*(q/v[3])^(3-v[2]);
insert([w, v[2], q], triprimes)
fi
od:
R;
MATHEMATICA
Select[Partition[Select[Range[12000], PrimeOmega[#] == 3 &], 2, 1], AllTrue[{#1 + #2, #2 - #1}, PrimeOmega[#] == 3 &] & @@ # &][[All, 1]] (* Michael De Vlieger, Sep 20 2023 *)
CROSSREFS
Cf. A014612.
Sequence in context: A248649 A050238 A115937 * A298381 A299248 A299457
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Sep 19 2023
STATUS
approved