A320867 Primes such that p + digitsum(p, base 6) is again a prime.

11, 19, 23, 31, 41, 53, 61, 79, 109, 137, 151, 167, 179, 229, 233, 263, 271, 331, 347, 359, 419, 439, 467, 541, 557, 587, 599, 607, 653, 719, 797, 809, 839, 863, 997, 1019, 1049, 1097, 1109, 1237, 1283, 1291, 1301, 1321, 1373, 1427, 1439, 1487, 1523, 1549, 1607, 1621, 1697, 1709, 1733, 1741, 1867

Offset: 1

Author

M. F. Hasler, Nov 06 2018

Keywords

• nonn
• base

Comments

Such primes exist only for an even base b. See A048519, A243441, A320866 and A320868 for the analog in base 10, 2, 4 and 8, respectively. Also, as in base 10, there are no such primes (except 7 and 11) when + is changed to -, see comment in A243442.

Examples

			11 = 6 + 5 = 15[6] (in base 6), and 11 + 1 + 5 = 17 is again prime.
		

Links

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

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), A320868 (analog for base 8).

Programs

Maple

filter:= n -> isprime(n) and isprime(n+convert(convert(n,base,6),`+`)):
select(filter, [seq(i,i=3..2000,2)]); # Robert Israel, Mar 22 2020

PARI

forprime(p=1,1999,isprime(p+sumdigits(p,6))&&print1(p","))