A368786 a(n) is the first prime p such that, if q are r are the next two primes, p + r, p + q, q + r and p + q + r all have n prime divisors, counted with multiplicity.

1559, 4073, 45863, 1369133, 82888913, 754681217, 118302786439

Offset: 3

Author

Zak Seidov and Robert Israel, Jan 05 2024

Keywords

• nonn
• more

Comments

a(n) is the first term p of A368785 such that A001222(A013634(p)) = n.

Examples

			a(5) = 45863 because 45863, 45869, 45887 are consecutive primes with
45863 + 45869 = 91732 = 2^2 * 17 * 19 * 71,
45863 + 45887 = 91750 = 2 * 5^3 * 367,
45869 + 45887 = 91756 = 2^2 * 7 * 29 * 113, and
45863 + 45869 + 45887 = 137619 = 3^4 * 1699
all have 5 prime divisors, counted with multiplicity, and 45763 is the least prime that works.
		

Crossrefs

Cf. A001222, A013634, A368785.

Programs

Maple

V:= Array(3..8): count:= 0:
p:= 2: q:= 3: r:= 5: v:= numtheory:-bigomega(q+r);
while count < 6 do
  p:= q; q:= r; r:= nextprime(r);
  w:= numtheory:-bigomega(q+r);
  if (w > 7 or V[w] = 0) and w = v and numtheory:-bigomega(p+r) = v and numtheory:-bigomega(p+q+r) = v then
    V[w]:= p; count:= count+1;
    fi;
  v:= w;
od:
convert(V,list);

Extensions

a(9) from Daniel Suteu, Jan 05 2024