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Difference between 3-almostprime(n) and 3-almostprime(n+2).
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%I #11 Jul 11 2015 10:27:19

%S 10,8,9,8,3,14,14,3,6,7,13,14,5,4,7,6,3,16,20,7,4,6,8,9,6,3,8,8,6,13,

%T 17,10,6,6,11,11,6,6,2,3,3,8,11,6,4,7,17,17,15,18,9,6,7,6,6,3,2,10,12,

%U 6,8,7,7,7,6,7,5,3,2,5,6,20,24,8,6,7,10,8,6,10,7

%N Difference between 3-almostprime(n) and 3-almostprime(n+2).

%C This is the 3-almost prime analog of what A113784 is for semiprimes and what A031131 is for primes. The minimum values in the sequence are 2 because we have, for example, the 3 consecutive 3-almost primes 170, 171, 172, so a(39) = A014612(41) - A014612(39) = 172 - 170 = 2. Equivalently, there are 2 consecutive 1 values of A114403 (3-almost prime gaps; first differences of A014612). This happens for elements of A113789 (numbers n such that n, n+1 and n+2 are 3-almost primes).

%F a(n) = A014612(n+2) - A014612(n).

%e a(1) = 10 because the difference between the first and third 3-almost primes is A014612(3) - A014612(1) = 18 - 8 = 10.

%e a(2) = A014612(4) - A014612(2) = 20 - 12 = 8.

%e a(3) = A014612(5) - A014612(3) = 27 - 18 = 9.

%Y Cf. A014612, A031131, A067813, A113784, A113789, A114403.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jan 21 2006

%E a(28) corrected by R. J. Mathar, Dec 22 2010