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Search: id:A090521
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| A090521 |
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Least k such that floor[n!/k] is prime. |
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2
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| 1, 2, 7, 7, 19, 22, 17, 74, 29, 76, 67, 49, 31, 43, 95, 59, 31, 41, 173, 79, 94, 73, 233, 107, 73, 29, 43, 201, 89, 274, 191, 349, 346, 199, 173, 249, 89, 373, 662, 197, 453, 166, 257, 865, 487, 254, 149, 852, 758, 389, 181, 151, 699, 634, 577, 542, 199, 61, 278, 482, 467
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Conjecture: There exists a number k such that for all n > k, a(n) is prime. Motivation: If p is the least prime >n then all the numbers from n to p-1 divide n!. And most of the numbers from p+1 to q also divide n! where q is the least prime > p,etc. and the dividend is composite in almost all cases.
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REFERENCES
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Amarnath Murthy, "Smaradache Reciprocal Function and an elementary inequality". Smarandache Notions Journal, Vol. 11, 2000.
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EXAMPLE
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a(5)=7 because the first values of floor(5!/k) for k=1,2,... are 120,60,40,30,24,20,17,15,13,12,... and among these the first prime number is 17, corresponding to k=7.
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MAPLE
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a:=proc(n) local p: p:=proc(k) if isprime(floor(n!/k))=true then k else fi end: [seq(p(m), m=1..1500)][1] end:seq(a(n), n=2..70); (Deutsch)
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CROSSREFS
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Cf. A090522.
Adjacent sequences: A090518 A090519 A090520 this_sequence A090522 A090523 A090524
Sequence in context: A021040 A003061 A087385 this_sequence A090523 A011416 A086658
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 07 2003
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 18 2005
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