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A111502
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Numbers n such that (n+j)^3-(n+j)^2+1 are primes for j=0 to 3.
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1
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33, 48, 203, 6648, 27048, 63293, 80288, 168348, 194298, 201178, 218888, 280103, 310828, 313668, 315448, 341893, 375298, 405958, 440643, 479668, 520058, 611868, 615893, 628068, 632533, 666973, 812888, 882728, 883643, 941143, 950983, 971158
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OFFSET
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1,1
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LINKS
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EXAMPLE
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33^3-33^2+1=34849 prime
34^3-34^2+1=38149 prime
35^3-35^2+1=41651 prime
36^3-36^2+1=45361 prime so n(1)=33
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MATHEMATICA
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fQ[n_] := Block[{j = {0, 1, 2, 3}}, Union@PrimeQ[(n + j)^3 - (n + j)^2 + 1] == {True}]; t = {}; Do[ If[ fQ[n], AppendTo[t, n]], {n, 1005807}] (* Robert G. Wilson v *)
slv[n_]:=x/.Solve[x^3-x^2+1==n, x][[1]]; slv/@(Transpose[Select[ Partition[ Table[ n^3-n^2+1, {n, 980000}], 4, 1], And@@PrimeQ[#]&]][[1]]) (* Harvey P. Dale, May 03 2014 *)
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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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