login
A320869
Primes such that p + digitsum(p, base 16) is again a prime.
1
17, 19, 23, 29, 31, 53, 59, 89, 127, 149, 151, 157, 179, 181, 211, 223, 241, 251, 263, 269, 331, 359, 367, 397, 419, 431, 449, 457, 461, 463, 487, 541, 563, 571, 593, 599, 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
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
17 = 16 + 1 = 11[16] (in base 16), and 17 + 1 + 1 = 19 is again prime.
MAPLE
digsum:= (n, b) -> convert(convert(n, base, b), `+`):
select(p -> isprime(p) and isprime(p+digsum(p, 16)), [2, seq(i, i=3..1000, 2)]); # Robert Israel, Nov 07 2018
PROG
(PARI) forprime(p=1, 1999, isprime(p+sumdigits(p, 16))&&print1(p", "))
CROSSREFS
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).
Sequence in context: A126769 A092216 A180948 * A187372 A106933 A191041
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Nov 06 2018
STATUS
approved