A091366 Primes p such that the sum of the cubes of the digits of p is prime.

11, 101, 113, 131, 139, 151, 193, 199, 223, 227, 241, 263, 269, 281, 283, 311, 337, 353, 359, 373, 421, 449, 461, 463, 487, 557, 577, 593, 599, 641, 643, 661, 733, 757, 821, 823, 827, 829, 883, 887, 919, 953, 991, 997, 1013, 1031, 1039, 1051, 1093, 1103, 1123

Offset: 1

Author

Chuck Seggelin, Jan 03 2004

Keywords

• base
• nonn

Comments

Apparently, in most cases the sum of the digits of such primes is also prime, see A091365 for the exceptions.

I conjecture the contrary: the relative density of numbers in this sequence with prime digit sum is 0. - Charles R Greathouse IV, Sep 08 2010

Examples

			a(1)=11 because 1^3 + 1^3 = 2 which is prime. a(10)=227 because 2^3 + 2^3 + 7^3 = 359 which is prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A046704 (primes whose digits sum to a prime) A052034 (primes whose digits squared sum to a prime) A091365 (primes whose digits cubed sum to a prime but whose digits do not sum to a prime).

Programs

Mathematica

Select[Prime[Range[2, 200]], PrimeQ[Total[IntegerDigits[#]^3]]&] (* Vincenzo Librandi, Apr 13 2013 *)

PARI

is(n)=my(v);if(!isprime(n),return(0));v=eval(Vec(Str(n)));isprime(sum(i=1,#v,v[i]^3)) \\ Charles R Greathouse IV, Sep 08 2010

Extensions

a(44) = 997 inserted by Charles R Greathouse IV, Sep 08 2010