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Search: id:A052248
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| A052248 |
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Greatest prime divisor of all composite numbers between p and next prime. |
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+0
20
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| 2, 3, 5, 3, 7, 3, 11, 13, 5, 17, 19, 7, 23, 17, 29, 5, 31, 23, 3, 37, 41, 43, 47, 11, 17, 53, 3, 37, 61, 43, 67, 23, 73, 5, 31, 79, 83, 43, 89, 5, 61, 3, 97, 11, 103, 109, 113, 19, 29, 79, 5, 83, 127, 131, 89, 5, 137, 139, 47, 97, 151, 103, 13, 157, 163, 167, 173, 29, 13
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Or, largest of all prime factors of the numbers between prime(n) and prime(n+1).
a(n) = 3, 5, 7, 11, 13 iff prime(n) is in A059960, A080185, A080186, A080187, A080188 respectively. This sequence defines a mapping f of primes > 2 to primes (cf. A080189) and f(p) < p holds for all p > 2. - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 10 2003
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..1000
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FORMULA
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a(n) = max(prime(n) < k < prime(n+1), A006530(k)).
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EXAMPLE
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a(8) = 11 since 20 = 2*2*5, 21 = 3*7, 22 = 2*11 are the numbers between prime(8) = 19 and prime(9) = 23.
For n=9, n-th prime is 23, composites between 23 and next prime are 24 25 26 27 29 of which largest prime divisor is 13, so a(9)=13.
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MATHEMATICA
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g[n_] := Block[{t = Range[Prime[n] + 1, Prime[n + 1] - 1]}, Max[First /@ Flatten[ FactorInteger@t, 1]]]; Table[ g[n], {n, 2, 72}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 08 2006)
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PROGRAM
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(PARI) forprime(p=3, 360, q=nextprime(p+1); m=0; for(j=p+1, q-1, f=factor(j); a=f[matsize(f)[1], 1]; if(m<a, m=a)); print1(m, ", "))
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CROSSREFS
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Cf. A006530, A059960, A080185, A080186, A080187, A080188, A080189.
Cf. A052180.
Sequence in context: A108396 A117367 A080184 this_sequence A092386 A117369 A117366
Adjacent sequences: A052245 A052246 A052247 this_sequence A052249 A052250 A052251
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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