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A320867
Primes such that p + digitsum(p, base 6) is again a prime.
4
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
1,1
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.
LINKS
EXAMPLE
11 = 6 + 5 = 15[6] (in base 6), and 11 + 1 + 5 = 17 is again prime.
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
PROG
(PARI) forprime(p=1, 1999, isprime(p+sumdigits(p, 6))&&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), A320868 (analog for base 8).
Sequence in context: A136435 A246428 A121658 * A165947 A129517 A287061
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Nov 06 2018
STATUS
approved