OFFSET
1,1
COMMENTS
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).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
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.
MATHEMATICA
pnpQ[n_]:=Module[{idn=IntegerDigits[n]}, !PrimeQ[Total[idn]]&&PrimeQ[ Total[ idn^4]]]; Select[Prime[Range[4000]], pnpQ] (* Harvey P. Dale, Apr 26 2018 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Jan 03 2004
STATUS
approved