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 A180245 n-th natural number m such that m and m+2 are both divisible by exactly n primes (counted with multiplicity). 0
 3, 33, 42, 196, 918, 6640, 24750, 246078, 781248, 6565374, 25227774, 165009150, 673932798, 5268548608, 25737162750, 179511912448, 818179991550, 4228689854464, 26455088693248, 104384041582590, 820632501420030 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Main diagonal A[n,n] of A[k,n] = n-th natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity). This is the main diagonal of the array mentioned in A180117, A180150, and A180151. Row 1 = A001359 = the lesser of twin primes. Row 2 = A092207 = Numbers n such that n and n+2 are semiprimes. Row 3 = A180117 = m and m+2 are both divisible by exactly 3 primes (counted with multiplicity). Row 4 = A180150 = m and m+2 are both divisible by exactly 4 primes (counted with multiplicity). Row 5 = A180151 = m and m+2 are both divisible by exactly 5 primes (counted with multiplicity). LINKS EXAMPLE a(1) = 3 because 3 is the first natural number m such that m and m+2 are both divisible by exactly 1 primes (i.e. the first of the lesser of twin primes. a(2) = 33 because that is the 2nd natural number m such that m and m+2 are both divisible by exactly 2 primes (i.e. 33 = 3 * 11 is semiprime and when 2 is added becomes 35 = 5 * 7 which is also semiprimes) the 1st such being 4. CROSSREFS Cf. A001359, A092207, A180117, A180150, A180151. Sequence in context: A284064 A101968 A103862 * A084502 A248397 A069165 Adjacent sequences:  A180242 A180243 A180244 * A180246 A180247 A180248 KEYWORD nonn AUTHOR Jonathan Vos Post, Aug 19 2010 EXTENSIONS Corrected and extended by Jack Brennen, D. S. McNeil and Ray Chandler, Aug 19 2010 a(16)-a(21) from Donovan Johnson, Aug 27 2010 STATUS approved

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Last modified May 13 18:08 EDT 2021. Contains 343865 sequences. (Running on oeis4.)