A320869 - OEIS

%I #9 Nov 08 2018 03:27:24

%S 17,19,23,29,31,53,59,89,127,149,151,157,179,181,211,223,241,251,263,

%T 269,331,359,367,397,419,431,449,457,461,463,487,541,563,571,593,599,

%U 601,631,659,661,701,733,761,769,809,811,839,907,911,941,971,997,1049,1087,1109,1171,1201,1237,1283,1289,1291

%N Primes such that p + digitsum(p, base 16) is again a prime.

%C Such primes exist only for an even base b. See A048519, A243441, A320866, A320867 and A320868 for the analog in base 10, 2, 4, 6 and 8, respectively. Also, as in base 10, there are no such primes when + is changed to -, see comment in A243442.

%H Robert Israel, <a href="/A320869/b320869.txt">Table of n, a(n) for n = 1..10000</a>

%e 17 = 16 + 1 = 11[16] (in base 16), and 17 + 1 + 1 = 19 is again prime.

%p digsum:= (n,b) -> convert(convert(n,base,b),`+`):

%p select(p -> isprime(p) and isprime(p+digsum(p,16)), [2,seq(i,i=3..1000,2)]); # _Robert Israel_, Nov 07 2018

%o (PARI) forprime(p=1,1999,isprime(p+sumdigits(p,16))&&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)), A320866 (analog for base 4), A320867 (analog for base 6), A320868 (analog for base 8).

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Nov 06 2018