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%I #15 Feb 06 2020 15:28:15
%S 5,7,13,17,19,37,59,67,97,127,173,193,223,233,277,359,379,439,499,563,
%T 569,599,607,631,653,691,733,769,811,821,829,877,919,929,937,967,1009,
%U 1019,1087,1093,1163,1193,1213,1223,1229,1297,1319,1373,1399,1423,1481,1483,1559,1571,1597,1613,1619,1627,1657,1699,1733,1777
%N Primes such that p + digitsum(p, base 4) is again a prime.
%C Such primes exist only for even bases b. See A243441, A320867, A320868 and A048519 for the analog in base 2, 6, 8 and 10, respectively. Also, as in base 10, there are no such primes (except 5 and 7) when + is changed to -, see comment in A243442.
%H Harvey P. Dale, <a href="/A320866/b320866.txt">Table of n, a(n) for n = 1..1000</a>
%e 5 = 4 + 1 = 11[4] (in base 4), and 5 + 1 + 1 = 7 is again prime.
%t Select[Prime[Range[300]],PrimeQ[#+Total[IntegerDigits[#,4]]]&] (* _Harvey P. Dale_, Feb 06 2020 *)
%o (PARI) forprime(p=1,1999,isprime(p+sumdigits(p,4))&&print1(p","))
%Y Cf. A047791, A048519 (base 10 analog), A048520, A006378, A107740, A243441 (base 2 analog: p + Hammingweight(p) is prime), A243442 (analog for p - Hammingweight(p)), A320867 (analog for base 6), A320868 (analog for base 8).
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Nov 06 2018
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