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A175767
List of pairs of "twin numbers": Omega(n) = Omega(n - 2^Omega(n)), where Omega is A001222.
0
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).
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Rewritten by Charles R Greathouse IV, Sep 03 2010
STATUS
approved