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A247278
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Least integer k > 0 such that k*n - prime(k) is a square.
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3
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1, 1, 4, 29, 1, 3, 4, 43, 3, 1, 5, 37, 2, 5, 9, 19, 1, 267, 22, 23, 4, 3, 43, 57, 2, 1, 46, 19, 20, 5, 4, 23, 440, 3, 5, 162, 1, 7, 20, 499, 2, 74, 4, 128, 29, 9, 927, 215, 156, 1, 96, 91, 7, 1058, 73, 162, 3, 763, 5
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OFFSET
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2,3
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COMMENTS
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Conjecture: a(n) exists for any n > 1.
Note that k*n - prime(k) < 0 if k > e^(n + 1).
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 29 since 29 * 5 - prime(29) = 145 - 109 = 6^2.
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MATHEMATICA
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SQ[n_] := IntegerQ[Sqrt[n]]
Do[k = 1; Label[aa]; If[SQ[k * n - Prime[k]], Print[n, " ", k]; Goto[bb]]; k = k + 1; Goto[aa]; Label[bb]; Continue, {n, 2, 60}]
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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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