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A091368
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Primes p such that the sum of the digits of p is not prime, but the sum of each digit raised to the 4th power is prime.
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1
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1699, 2689, 6199, 6829, 6991, 7477, 8089, 8269, 8629, 9619, 12589, 15289, 19069, 19609, 20599, 20959, 21589, 21859, 23857, 25189, 25819, 25873, 25981, 27259, 27529, 27583, 28069, 28537, 28573, 28591, 28753, 29059, 29527, 29581, 29851
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OFFSET
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1,1
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COMMENTS
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Apparently, for primes such that each digit raised to the 4th power 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 760 primes whose digits raised to the 4th power sum to a prime. Of these, only 106 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 A091367 (primes whose digits raised to the 4th power 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)=1699 because 1+6+9+9 = 25 which is not prime, but 1^4 + 6^4 + 9^4 + 9^4 = 14419 which is prime.
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MATHEMATICA
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pnpQ[n_]:=Module[{idn=IntegerDigits[n]}, !PrimeQ[Total[idn]]&&PrimeQ[ Total[ idn^4]]]; Select[Prime[Range[4000]], pnpQ] (* Harvey P. Dale, Apr 26 2018 *)
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CROSSREFS
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Cf. A046704 (primes whose digits sum to a prime) A091367 (primes whose digits raised to the 4th power sum to a prime) A052034 and A091362 (same observation for digits squared) A091366 and A091365 (same observation for digits cubed).
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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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