A320869 Primes such that p + digitsum(p, base 16) is again a prime.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A320866 A320867 A320868 * A320870 A320871 A320872

Keyword

nonn,base

Author

M. F. Hasler, Nov 06 2018

Status

approved