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A060698
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The sum of the first n composite numbers minus 1 is a prime.
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1
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1, 3, 11, 15, 22, 39, 51, 57, 66, 67, 71, 79, 98, 105, 108, 109, 115, 118, 119, 125, 135, 150, 151, 152, 156, 160, 169, 200, 201, 205, 211, 223, 228, 241, 271, 281, 282, 291, 312, 315, 322, 331, 341, 350, 372, 382, 385, 395, 401, 420, 433, 461, 482, 498, 544
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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Composite[ n_Integer ] := (k = n + PrimePi[ n ] + 1; While[ k - PrimePi[ k ] - 1 != n, k++ ]; k); Select[ Range[ 1000 ], PrimeQ[ Sum[ Composite[ k ], {k, 1, #} ] - 1 ] & ]
Position[Accumulate[Select[Range[700], CompositeQ]]-1, _?PrimeQ]//Flatten (* Harvey P. Dale, Jul 20 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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