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A045985
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a(n) = least k such that sum of first k primes is n times a prime.
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2
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1, 3, 10, 5, 3, 123, 8, 15, 20, 147, 8, 97, 92, 5, 414, 27, 120, 739, 144, 9, 86, 69, 858, 99, 62, 61, 26, 33, 7, 57, 456, 11, 76, 13, 180, 207, 58, 23, 166, 17, 38, 339, 10, 693, 242, 23, 1162, 169, 440, 9, 374, 117, 682, 187, 1284, 683, 70, 281, 48
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OFFSET
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1,2
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LINKS
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EXAMPLE
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a(3) = 10 because the partial sum of the first 10 primes is 3*43 = 129.
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MATHEMATICA
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a[n_] := Catch[For[p=0; sp=0; k=1, True, k++, p = NextPrime[p]; sp = sp+p; If[PrimeQ[sp/n], Throw[k]]]]; Table[a[n], {n, 1, 59}] (* Jean-François Alcover, Nov 13 2012 *)
Module[{nn=1500, p, t}, p=Accumulate[Prime[Range[nn]]]; t=Thread[{Range[ nn], p}]; Table[SelectFirst[t, PrimeQ[ #[[2]]/n]&], {n, 60}]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 16 2020 *)
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PROG
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(Haskell)
a045985 n = head [k | (k, x) <- zip [1..] a007504_list,
let (y, r) = divMod x n, r == 0, a010051' y == 1]
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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