A176872 Prime numbers p such that p-LargestSquare is prime and p-LargestCube is also prime, (LargestSquare <= p, LargestCube <= p).

3, 11, 19, 67, 71, 83, 107, 227, 263, 269, 613, 619, 1031, 1061, 1163, 1193, 1223, 1307, 1787, 1801, 1811, 1831, 1979, 1997, 2129, 4099, 4127, 4133, 4139, 4157, 4373, 4409, 4463, 4637, 4643, 4703, 5843, 5849, 5879, 5903, 6089, 6101, 6113, 6143, 6163, 6211

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 27 2010

Keywords

• nonn

Comments

11-3^2=2;11-2^3=3, 19-4^2=3,19-2^3=11,..

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A135932, A176864, A176865, A176870, A176871

Programs

Mathematica

lst={};Do[p2=n-Floor[Sqrt[n]]^2;p3=n-Floor[n^(1/3)]^3;If[PrimeQ[p2]&&PrimeQ[p3]&&PrimeQ[n],AppendTo[lst,n]],{n,8!}];lst
plsplcQ[p_]:=AllTrue[{p-Floor[Sqrt[p]]^2,p-Floor[Surd[p,3]]^3},PrimeQ]; Select[ Prime[ Range[1000]],plsplcQ] (* Harvey P. Dale, Jul 03 2022 *)