A175767 List of pairs of "twin numbers": Omega(n) = Omega(n - 2^Omega(n)), where Omega is A001222.

3, 5, 5, 7, 6, 10, 11, 13, 10, 14, 17, 19, 12, 20, 21, 25, 22, 26, 20, 28, 29, 31, 34, 38, 35, 39, 24, 40, 41, 43, 42, 50, 44, 52, 51, 55, 40, 56, 59, 61, 58, 62, 65, 69, 71, 73, 68, 76, 70, 78, 48, 80, 82, 86, 87, 91, 91, 95, 84, 100, 101, 103, 88, 104, 107, 109, 102, 110, 80, 112, 111

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 01 2010

Keywords

• nonn

Comments

The k-primes = numbers that are divisible by exactly k primes (counted with multiplicity).

Examples

			"Twin numbers" are (3, 5), (5, 7), (6, 10), (11, 13), (10, 14), (17, 19), (12, 20), (21, 25), (22, 26), (20, 28), (29, 31), (34, 38), (35, 39), (24, 40), (41, 43), (42, 50), (44, 52), (51, 55), (40, 56), (59, 61), (58, 62), (65, 69), (71, 73), ...
		

Crossrefs

Cf. A175766, A001222, A077800, A175612, A175765.

Programs

Mathematica

Flatten[{#[[3]],#[[1]]}&/@Select[Table[{n,PrimeOmega[n],n-2^PrimeOmega[n],PrimeOmega[ n-2^PrimeOmega[n]]},{n,150}],#[[2]]==#[[4]]&]] (* Harvey P. Dale, Mar 23 2024 *)

Formula

a(2n+1) = A175766(n) = a(2n) + 2^A001222(a(2n+1)).

Extensions

Rewritten by Charles R Greathouse IV, Sep 03 2010