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

1,1

Comments

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

Links

Table of n, a(n) for n=1..71.

Formula

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

Example

"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), ...

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 *)

Crossrefs

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

Sequence in context: A285204 A086269 A057952 * A111800 A190136 A360635

Adjacent sequences: A175764 A175765 A175766 * A175768 A175769 A175770

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 01 2010

Extensions

Rewritten by Charles R Greathouse IV, Sep 03 2010

Status

approved