OFFSET
1,1
COMMENTS
EXAMPLE
p=3 is in the sequence because the distance p-1=2 to the cube 1^3 below 3, and also the distance 8-p=5 to the cube 8=2^3 above p are prime.
p=127 is in the sequence because the distance p-125=2 to the cube 125=5^3 below p, and also the distance 216-p=89 to the cube 216=6^3 above p, are prime.
MATHEMATICA
Clear[f, lst, p, n]; f[n_]:=IntegerPart[n^(1/3)]; lst={}; Do[p=Prime[n]; If[PrimeQ[p-f[p]^3]&&PrimeQ[(f[p]+1)^3-p], AppendTo[lst, p]], {n, 9!}]; lst
dncQ[n_]:=Module[{c=Floor[Surd[n, 3]]}, AllTrue[{n-c^3, (c+1)^3-n}, PrimeQ]]; Select[Prime[Range[230000]], dncQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 16 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Aug 05 2009
EXTENSIONS
Edited, first 5 entries checked by R. J. Mathar, Aug 12 2009
Two more terms (a(8) and a(9)) from Harvey P. Dale, Oct 16 2016
STATUS
approved