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A354085
Least prime q > p = prime(n) such that Omega(p+q) = 3.
1
43, 5, 7, 11, 17, 17, 53, 23, 29, 37, 37, 41, 61, 59, 67, 61, 71, 103, 71, 83, 97, 103, 89, 97, 139, 137, 109, 131, 113, 131, 131, 137, 149, 151, 167, 167, 181, 191, 199, 181, 191, 193, 197, 211, 229, 211, 223, 229, 271, 241, 241, 269, 257, 257, 277, 271, 313
OFFSET
1,1
LINKS
EXAMPLE
n=1: prime(1) + a(1) = 2 + 43 = 45 = 3*3*5;
n=2: prime(2) + a(2) = 3 + 5 = 8 = 2*2*2;
n=3: prime(3) + a(3) = 5 + 7 = 12 = 2*2*3;
n=4: prime(4) + a(4) = 7 + 11 = 18 = 2*3*3;
n=5: prime(5) + a(5) = 11 + 17 = 28 = 2*2*7;
each is the product of 3 primes.
MAPLE
f:= proc(n) local p, q;
p:= ithprime(n);
q:= p;
do
q:= nextprime(q);
until numtheory:-bigomega(p+q)=3;
q
end proc:
map(f, [$1..100]); # Robert Israel, Jan 08 2024
MATHEMATICA
s = {43}; p = 2; Do[p = NextPrime[p]; q = p; While[3 != PrimeOmega[p + q], q = NextPrime[q]]; AppendTo[s, q], {200}]; s
CROSSREFS
Cf. A000040, A001222 (Omega).
Sequence in context: A292996 A107814 A093762 * A156677 A097398 A225210
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 05 2022
STATUS
approved