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

1,1

Comments

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

Links

Table of n, a(n) for n=1..56.

Example

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).

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

Crossrefs

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

Sequence in context: A079829 A096090 A037286 * A166534 A126727 A340618

Adjacent sequences: A166530 A166531 A166532 * A166534 A166535 A166536

Keyword

base,nonn

Author

Zak Seidov, Oct 16 2009

Extensions

Edited by Charles R Greathouse IV, Mar 23 2010

Status

approved