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%I #12 Feb 15 2014 11:14:00
%S 997,1699,2887,5569,5659,5839,5857,6199,6883,6991,7477,8287,8539,8863,
%T 8999,9619,9907,11779,11887,13399,13669,14479,14767,14947,15559,16369,
%U 16477,16693,16747,16963,17377,17449,17467,17737,17791,17827,17881
%N Primes p such that the sum of the digits of p is not prime, but the sum of the squares of the digits of p is prime.
%C Apparently if the squares 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 1558 primes p such that the squares of the digits of p sum to a prime. Of these, only 360 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 A052034 (primes whose digits squared sum to a prime) that do not also appear in A046704 (primes whose digits sum to a prime).
%H Vincenzo Librandi, <a href="/A091362/b091362.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1)=997 because 9+9+7 = 25 which is not prime, but 9^2+9^2+7^2 = 211 which is prime.
%t ssdQ[n_]:=Module[{idn=IntegerDigits[n]},!PrimeQ[Total[idn]]&&PrimeQ[ Total[ idn^2]]]; Select[Prime[Range[2100]],ssdQ] (* _Harvey P. Dale_, Jun 28 2011 *)
%Y Cf. A046704 (primes whose digits sum to a prime), A052034 (primes whose digits squared sum to a prime).
%K base,nonn
%O 1,1
%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Jan 03 2004
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