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Search: id:A127165
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| A127165 |
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a(n) = the maximum prime S possible, if S = product of b(k)'s + product of c(k)'s, where the distinct positive integers <= n are partitioned into the two sets {b(k)} and {c(k)}. a(n) = 0 if no prime S exists for that n. |
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+0
3
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| 2, 2, 3, 7, 11, 43, 149, 1013, 8069, 0, 0, 39916801, 43545611, 566092811, 7925299211, 118879488011, 1609445376013, 32335220736011, 44771844096143, 582033973248209, 221172909834240011, 3930072474746880013
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(0)=a(1)=2 because the product over the empty set is defined here as 1. For S to be a prime, the positive integers <= n, except 1 and the primes > n/2, must all be together in either {b(k)} or {c(k)}. If p is a prime where n/2 < p <= n, then it is possible that p is in either product of the S sum, as can 1. Terms calculated by Edwin Clark.
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LINKS
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Ray Chandler, Table of n, a(n) for n=0..100
Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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For n = 6 we have the only prime S (and so, the maximum prime S) with S = 1*2*3*4*6 + 5 = 149.
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MATHEMATICA
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f[n_] := Block[{d = Divisors[Times @@ Select[Range[n], PrimeQ[ # ] && 2# > n &]]}, Select[Union[d + n!/d], PrimeQ]]; If[ # == {}, 0, Last[ # ]] & /@ Array[f, 30, 0] (*Chandler*)
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CROSSREFS
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Cf. A127166, A128199.
Sequence in context: A036060 A065383 A087384 this_sequence A100683 A153940 A049905
Adjacent sequences: A127162 A127163 A127164 this_sequence A127166 A127167 A127168
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Jan 06 2007
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EXTENSIONS
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a(21)-a(35) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 2007
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