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Search: id:A072821
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| A072821 |
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Largest prime that can appear in any representation of n as an arithmetic mean of distinct primes. |
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+0
2
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| 1, 1, 7, 7, 13, 13, 23, 19, 29, 29, 43, 37, 53, 47, 71, 61, 79, 73, 103, 89, 113, 109, 139, 127, 157, 139, 179, 163, 199, 181, 223, 199, 241, 227, 271, 241, 293, 271, 317, 293, 349, 317, 379, 349, 409, 379, 439, 409, 463, 439, 503, 463, 523, 499, 571, 523, 601
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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Thanks to John Layman for inspiration.
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LINKS
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Reinhard Zumkeller, Representing integers as arithmetic means of primes
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EXAMPLE
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a(6)=13, as 13 is the largest prime in 6 = (5+7)/2 = (2+3+13)/3 = (2+5+11)/3 = (2+3+5+7+13)/5.
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MAPLE
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Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 03 2009: (Start)
sp:= proc(i) option remember; `if` (i=1, 2, sp(i-1) +ithprime(i)) end:
b:= proc(n, i, t) option remember; local h; if n<0 then 0 elif n=0 then `if` (t=0, 1, 0) elif i=2 then `if` (n=2 and t=1, 2, 0) else `if` (b(n-i, prevprime(i), t-1)>0, i, b(n, prevprime(i), t)) fi end:
a:= proc(n) local s, k; s:= 1; for k from 2 while sp(k)/k<=n do s:= max (s, b(k*n, nextprime (k*n -sp(k-1)-1), k)) od: s end: seq (a(n), n=2..40); (End)
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CROSSREFS
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Cf. A072701.
Sequence in context: A003883 A116934 A143429 this_sequence A038589 A109539 A109541
Adjacent sequences: A072818 A072819 A072820 this_sequence A072822 A072823 A072824
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 15 2002
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 03 2009
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