A335652 Numbers k such that Omega(k+1) = Omega(k) + 2, where Omega(k) = A001222(k) is the number of prime factors of k with multiplicity.

7, 11, 15, 17, 19, 29, 35, 39, 41, 43, 55, 67, 87, 97, 101, 109, 113, 134, 137, 155, 163, 173, 175, 181, 183, 203, 207, 209, 211, 219, 229, 241, 242, 247, 249, 257, 259, 279, 281, 283, 295, 305, 314, 317, 327, 329, 331, 337, 339, 341, 351, 353, 371, 373, 401, 404, 409, 413, 433, 455

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

7 is prime, Omega(7) = 1, 7 + 1 = 8 = 2*2*2, Omega(8) = 3.

Maple

Omegas:= [seq(numtheory:-bigomega(i), i=1..1001)]:
select(i -> Omegas[i]+2=Omegas[i+1], [$1..1000]); # Robert Israel, Jun 16 2020

Mathematica

m = 2; s = {}; Do[If[PrimeOmega[x + 1] == PrimeOmega[x] + m, AppendTo[s, x]], {x, 500}]; s
Position[Partition[PrimeOmega[Range[500]], 2, 1], _?(#[[1]]==#[[2]]-2&), 1, Heads-> False]//Flatten (* Harvey P. Dale, Jul 04 2021 *)

Crossrefs

Omega(k+1) = Omega(k) + m: A045920 (m = 0), A076156 (m = 1).

Cf. A001222, A335655. Contains A063639.

Sequence in context: A144931 A166257 A192992 * A176852 A248630 A130569

Adjacent sequences: A335649 A335650 A335651 * A335653 A335654 A335655

Keyword

nonn

Author

Zak Seidov, Jun 16 2020

Status

approved