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A176881
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a(n)=p-q for n-th product of 2 distinct primes p and q (q<p).
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4
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1, 3, 5, 2, 4, 9, 11, 8, 15, 2, 17, 10, 21, 14, 6, 16, 27, 29, 8, 20, 35, 4, 39, 12, 41, 26, 6, 28, 45, 14, 51, 34, 18, 57, 10, 59, 38, 40, 12, 65, 44, 69, 2, 24, 71, 26, 77, 50, 16, 81, 56, 87, 58, 32, 6, 95, 64, 99, 22, 36, 101, 8, 68, 105, 38, 24, 107, 70, 4, 111, 42, 76, 6, 80
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OFFSET
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1,2
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COMMENTS
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Where products of two distinct primes are in A006881.
If Polignac's conjecture is true, then every even positive integer occurs infinitely many times in this sequence. - Clark Kimberling, Apr 25 2016
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LINKS
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EXAMPLE
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a(1)=1 because 1=3-2 for A006881(1)=6=3*2; a(2)=3 because 3=5-2 for A006881(2)=10=5*2.
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MAPLE
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A006881 := proc(n) if n = 1 then 6; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 and nops(numtheory[factorset](a)) =2 then return a; end if; end do: end if; end proc:
A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:
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MATHEMATICA
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mx = 350; t = Sort@Flatten@Table[Prime[n]*Prime[m], {n, Log[2, mx/3]}, {m, n + 1, PrimePi[mx/Prime[n]]}]; (* A006881, _Robert G.Wilson v_, Feb 07 2012 *)
u = Table[FactorInteger[t[[k]]][[1]], {k, 1, Length[t]}];
u1 = Table[u[[k]][[1]], {k, 1, Length[t]}] (* A096916 *)
v = Table[FactorInteger[t[[k]]][[2]], {k, 1, Length[t]}];
v1 = Table[v[[k]][[1]], {k, 1, Length[t]}] (* A070647 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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