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A201050
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C(n#, (n-1)#), where n# is the primorial A034386(n), the product of primes <= n.
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0
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OFFSET
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1,2
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COMMENTS
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Next term a(11) has 305 digits.
a(n) = 1 if and only if n is nonprime. When n is composite, n# and (n-1)# are the same, and since C(n, n) = 1, a(n) = 1 as well.
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LINKS
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FORMULA
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a(n) = binomial(n#, (n-1)#).
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EXAMPLE
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a(3) = 15 because the 3rd primorial is 6, the (3-1)th primorial is 2, and C(6, 2) = 15.
a(5) = (product_{i=5#-3#+1..5#} a(i))/(3#)! = 25*26*27*28*29*30/6! = 593775.
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MATHEMATICA
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lst = {}; Do[AppendTo[lst, Binomial[Product[Prime[i], {i, n}], Product[Prime[i], {i, n - 1}]]]; AppendTo[lst, Table[1, {Prime[n + 1] - Prime[n] - 1}]], {n, 6}]; Prepend[Flatten[lst], 1]
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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