A166533 Numbers whose cube is a concatenation of exactly three primes (leading zeros allowed).

13, 15, 18, 29, 33, 38, 39, 43, 45, 48, 55, 59, 63, 68, 73, 83, 91, 95, 98, 103, 108, 111, 117, 125, 131, 137, 148, 149, 161, 163, 171, 173, 175, 177, 179, 217, 233, 235, 237, 241, 258, 259, 275, 278, 289, 293, 295, 297, 321, 337, 339, 357, 377, 378, 388, 391

Offset: 1

Author

Zak Seidov, Oct 16 2009

Keywords

• base
• nonn

Comments

The three primes are not necessarily all distinct. All even terms k are == 8 (mod 10) (and hence k^3 == 2 (mod 10)).

Examples

			13^3 =   2197 => { 2,  19,  7};
15^3 =   3375 => { 3,  37,  5};
18^3 =   5832 => { 5,  83,  2};
43^3 =  79507 => {79,   5, 07} (first case with leading zero);
48^3 = 110592 => {11, 059,  2} (next case with leading zero).
		

Crossrefs

Cf. A166534 (version with leading zeros not allowed), A038840 Cubes that are concatenations of primes.

Programs

Mathematica

s={};Do[id=IntegerDigits[n^3];Le=Length@id; Do[t=FromDigits/@{Take[id,k],Take[id,{k+1,m}],Take[id,m-Le]}; If[PrimeQ[t]=={True,True,True},AppendTo[s,n];Goto[ne]],{k,Le-2},{m,k+1,Le-1}];Label[ne],{n,5,800}];s

Extensions

Edited by Charles R Greathouse IV, Mar 23 2010