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A368615
Semiprimes k such that prime(k) - k and prime(k) + k are also semiprimes.
1
58, 74, 166, 226, 262, 326, 334, 478, 566, 694, 734, 802, 838, 886, 1114, 1142, 1294, 1382, 1514, 1574, 1894, 2038, 2078, 2138, 2858, 3254, 3274, 3314, 3578, 4286, 4306, 4426, 5102, 5242, 5386, 5398, 5578, 5806, 5906, 6022, 6046, 6362, 6866, 7094, 7142, 7246, 7274, 7438, 7694, 7838, 7886, 7934
OFFSET
1,1
COMMENTS
All terms are even.
LINKS
FORMULA
Numbers k such that A001222(k) = A001222(A000040(k) - k) = A001222(A000040(k) + k) = 2.
a(n) == 2 (mod 4). - Hugo Pfoertner, Jan 05 2024
EXAMPLE
a(3) = 166 is a term because the 166th prime is 983, and 166 = 2 * 83, 983 - 166 = 817 = 19 * 43, and 983 + 166 = 1149 = 3 * 383 are all semiprimes.
MAPLE
p:= 1: R:= NULL: count:= 0:
for k from 2 by 2 while count < 100 do
p:= nextprime(nextprime(p));
if isprime(k/2) and numtheory:-bigomega(k+p) = 2 and numtheory:-bigomega(p-k) = 2 then count:= count+1; R:= R, k fi
od:
R;
MATHEMATICA
s = {}; Do[If[{2, 2, 2} == PrimeOmega[{k, Prime[k] + k, Prime[k] - k}], AppendTo[s, k]], {k, 4, 10000}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Dec 31 2023
STATUS
approved