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Search: id:A132809
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| A132809 |
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First prime in a sequence of n consecutive odd primes with integral arithmetic mean. |
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+0
3
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| 3, 3, 5, 71, 5, 7, 17, 239, 13, 29, 5, 43, 23, 5, 5, 7, 7, 79, 17, 47, 11, 109, 73, 97, 53, 271, 13, 263, 23, 41, 61, 97, 101, 181, 41, 47, 13, 233, 13, 53, 13, 359, 151, 71, 61, 239, 73, 443, 859, 29, 131, 131, 61, 313, 101, 19, 151, 521, 3, 571, 31, 7, 79, 109, 97, 53, 53
(list; graph; listen)
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OFFSET
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2,1
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FORMULA
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a(n) = {min (prime(k)): sum_{i=0..n-1} prime(k+i) = 0 mod n, k>1 } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 27 2007
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EXAMPLE
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For n=2 we add prime(2)+prime(3)=3+5=8 which is already a multiple of n=2, so we add the first of the primes, 3, at a(n=2).
For n=5 we test 3+5+7+11+13=39 against being a multiple of n=5, then 5+7+11+13+17=53, then 7+11+13+17+19=67 etc. and find that 71+73+79+83+89=395 is a multiple. We place the smallest member in this sequence of 5 primes, 71, at a(n=5).
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MAPLE
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A132809 := proc(n) local i, j ; for i from 2 do if add( ithprime(i+j), j=0..n-1) mod n = 0 then RETURN(ithprime(i)) ; fi ; od: end: seq(A132809(n), n=2..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 27 2007
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CROSSREFS
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Cf. A132810-A132811.
Sequence in context: A123633 A110426 A093310 this_sequence A005882 A085572 A010609
Adjacent sequences: A132806 A132807 A132808 this_sequence A132810 A132811 A132812
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KEYWORD
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easy,nonn
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AUTHOR
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Enoch Haga (Enokh(AT)comcast.net), Sep 01 2007
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 27 2007
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