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A091362
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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.
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3
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997, 1699, 2887, 5569, 5659, 5839, 5857, 6199, 6883, 6991, 7477, 8287, 8539, 8863, 8999, 9619, 9907, 11779, 11887, 13399, 13669, 14479, 14767, 14947, 15559, 16369, 16477, 16693, 16747, 16963, 17377, 17449, 17467, 17737, 17791, 17827, 17881
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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a(1)=997 because 9+9+7 = 25 which is not prime, but 9^2+9^2+7^2 = 211 which is prime.
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MATHEMATICA
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ssdQ[n_]:=Module[{idn=IntegerDigits[n]}, !PrimeQ[Total[idn]]&&PrimeQ[ Total[ idn^2]]]; Select[Prime[Range[2100]], ssdQ] (* Harvey P. Dale, Jun 28 2011 *)
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CROSSREFS
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Cf. A046704 (primes whose digits sum to a prime), A052034 (primes whose digits squared sum to a prime).
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KEYWORD
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base,nonn
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AUTHOR
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Chuck Seggelin (barkeep(AT)plastereddragon.com), Jan 03 2004
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STATUS
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approved
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