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

Author

Zak Seidov, Jun 16 2020

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Cf. A001222, A335655. Contains A063639.

Programs

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 *)