A320868 Primes such that p + digitsum(p, base 8) is again a prime.

13, 29, 31, 41, 47, 61, 67, 71, 83, 97, 157, 193, 229, 241, 271, 283, 373, 397, 409, 431, 449, 467, 503, 587, 601, 607, 761, 787, 929, 971, 991, 1039, 1087, 1091, 1163, 1181, 1213, 1217, 1237, 1249, 1289, 1291, 1307, 1423, 1453, 1471, 1511, 1543, 1553, 1559, 1627, 1657, 1741, 1811, 1847, 1867, 1973, 1999

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 A320867 for the analog in base 10, 2, 4 and 6, respectively. Also, as in base 10, there are no such primes (except 11 and 13) when + is changed to -, see comment in A243442.

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), A320867 (analog for base 6).

Programs

Maple

digsum:= proc(n,b) convert(convert(n,base,b),`+`) end proc:
select(p -> isprime(p) and isprime(p+digsum(p,8)), [seq(i,i=3..10000,2)]); # Robert Israel, Nov 07 2018

PARI

forprime(p=1,1999,isprime(p+sumdigits(p,8))&&print1(p","))