A091365 Primes p such that the sum of the digits of p is not prime, but the sum of the cubes of the digits of p is prime.

997, 2797, 3499, 4993, 7297, 7477, 7927, 8089, 8999, 9277, 9349, 9439, 9907, 11689, 12697, 12967, 14479, 14767, 14929, 14947, 16189, 16477, 16729, 16747, 16927, 16981, 17449, 17467, 18169, 18691, 19249, 19267, 19429, 19447, 19681, 19861

Offset: 1

Author

Chuck Seggelin, Jan 03 2004

Keywords

• base
• nonn

Comments

Apparently if the cubes of the digits of a prime sum to a prime, it is more likely that the digits themselves also sum to a prime. In the first 10,000 primes there are 1969 primes p such that the cubes of the digits of p sum to a prime. Of these, only 358 are such that the sums of the digits are not prime. Interestingly, all of these primes have a digit sum of 25 or 35. Essentially this sequence is the terms of A091366 (primes whose digits cubed sum to a prime) that do not also appear in A046704 (primes whose digits sum to a prime).

Examples

			a(1)=997 because 9+9+7 = 25 which is not prime, but 9^3+9^3+7^3 = 1801 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) A091366 (primes whose digits squared sum to a prime).

Programs

Mathematica

ssdQ[n_]:= Module[{idn = IntegerDigits[n]}, !PrimeQ[Total[idn]]&&PrimeQ[Total[idn^3]]]; Select[Prime[Range[4000]], ssdQ] (* Vincenzo Librandi, Apr 17 2013 *)