A111502 Numbers n such that (n+j)^3-(n+j)^2+1 are primes for j=0 to 3.

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

Offset

1,1

Links

Table of n, a(n) for n=1..32.

Example

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

Mathematica

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 *)

Crossrefs

Sequence in context: A258698 A258697 A204373 * A080933 A328247 A020293

Adjacent sequences: A111499 A111500 A111501 * A111503 A111504 A111505

Keyword

nonn

Author

Pierre CAMI, Nov 16 2005

Extensions

a(6)-a(32) from Robert G. Wilson v, Nov 18 2005

Status

approved