A354085 Least prime q > p = prime(n) such that Omega(p+q) = 3.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A354082 A354083 A354084 * A354086 A354087 A354088

Keyword

nonn

Author

Zak Seidov, Jun 05 2022

Status

approved