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%I #6 Apr 26 2018 05:41:52
%S 1699,2689,6199,6829,6991,7477,8089,8269,8629,9619,12589,15289,19069,
%T 19609,20599,20959,21589,21859,23857,25189,25819,25873,25981,27259,
%U 27529,27583,28069,28537,28573,28591,28753,29059,29527,29581,29851
%N 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.
%C 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).
%H Harvey P. Dale, <a href="/A091368/b091368.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%t pnpQ[n_]:=Module[{idn=IntegerDigits[n]},!PrimeQ[Total[idn]]&&PrimeQ[ Total[ idn^4]]]; Select[Prime[Range[4000]],pnpQ] (* _Harvey P. Dale_, Apr 26 2018 *)
%Y 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).
%K base,nonn
%O 1,1
%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Jan 03 2004
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