OFFSET
1,1
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).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
EXAMPLE
a(1)=997 because 9+9+7 = 25 which is not prime, but 9^3+9^3+7^3 = 1801 which is prime.
MATHEMATICA
ssdQ[n_]:= Module[{idn = IntegerDigits[n]}, !PrimeQ[Total[idn]]&&PrimeQ[Total[idn^3]]]; Select[Prime[Range[4000]], ssdQ] (* Vincenzo Librandi, Apr 17 2013 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Jan 03 2004
STATUS
approved