OFFSET
1,1
COMMENTS
This would not work with semiprimes instead of triprimes: for consecutive primes p, q, it is impossible for p+q to be a semiprime.
First of three consecutive primes p, q, r such that (p+q)/2, (p+r)/2 and (q+r)/2 are all semiprimes.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 5237 is a term because 5237, 5261 and 5273 are consecutive primes with 5237 + 5261 = 10498 = 2 * 29 * 181, 5237 + 5273 = 10510 = 2 * 5 * 1051 and 5261 + 5273 = 10534 = 2 * 23 * 229 triprimes.
MAPLE
q:= 2: r:= 3: R:= NULL: count:= 0:
while count < 100 do
p:= q; q:= r; r:= nextprime(r);
if numtheory:-bigomega(p+q)=3 and numtheory:-bigomega(p+r)=3 and numtheory:-bigomega(q+r)=3
then R:= R, p; count:= count+1;
fi
od:
R;
MATHEMATICA
p = 2; q = 3; r = 5; s = {}; Do[If[{3, 3, 3} == PrimeOmega[{p + q, q + r, p + r}], AppendTo[s, p]]; p = q; q = r; r = NextPrime[r], {100000}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Apr 10 2023
STATUS
approved