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A247893
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Least integer k > 0 such that prime(k) - k*n is a square.
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2
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1, 1, 12, 35, 75, 181, 490, 1061, 2707, 6459, 15932, 40127, 100362, 251711, 637236, 1617181, 4124444, 10553419, 27066987, 69709706, 179992917, 465769804, 1208198534, 3140421726, 8179002096, 21338685437, 55762149044, 145935689364, 382465573484, 1003652347334
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OFFSET
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1,3
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COMMENTS
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Conjecture: a(n) exists for any n > 0.
See also A247278 for a related conjecture.
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LINKS
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EXAMPLE
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a(3) = 12 with prime(12) - 12*3 = 37 - 36 = 1^2.
a(21) = 179992917 with prime(179992917) - 179992917*21 = 3779851261 - 179992917*21 = 2^2.
a(22) = 465769804 with prime(465769804) - 465769804*22 = 10246935737 - 465769804*22 = 7^2.
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MATHEMATICA
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SQ[n_]:=IntegerQ[Sqrt[n]]
Do[k=1; Label[aa]; If[SQ[Prime[k]-k*n], Print[n, " ", k]; Goto[bb]]; k=k+1; Goto[aa]; Label[bb]; Continue, {n, 1, 18}]
lik[n_]:=Module[{k=1}, While[!IntegerQ[Sqrt[Prime[k]-k*n]], k++]; k]; Array[lik, 20] (* Harvey P. Dale, May 11 2019 *)
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CROSSREFS
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KEYWORD
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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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