A320866 Primes such that p + digitsum(p, base 4) is again a prime.

5, 7, 13, 17, 19, 37, 59, 67, 97, 127, 173, 193, 223, 233, 277, 359, 379, 439, 499, 563, 569, 599, 607, 631, 653, 691, 733, 769, 811, 821, 829, 877, 919, 929, 937, 967, 1009, 1019, 1087, 1093, 1163, 1193, 1213, 1223, 1229, 1297, 1319, 1373, 1399, 1423, 1481, 1483, 1559, 1571, 1597, 1613, 1619, 1627, 1657, 1699, 1733, 1777

Offset: 1

Author

M. F. Hasler, Nov 06 2018

Keywords

• nonn
• base

Comments

Such primes exist only for even bases b. See A243441, A320867, A320868 and A048519 for the analog in base 2, 6, 8 and 10, respectively. Also, as in base 10, there are no such primes (except 5 and 7) when + is changed to -, see comment in A243442.

Examples

			5 = 4 + 1 = 11[4] (in base 4), and 5 + 1 + 1 = 7 is again prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

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)), A320867 (analog for base 6), A320868 (analog for base 8).

Programs

Mathematica

Select[Prime[Range[300]],PrimeQ[#+Total[IntegerDigits[#,4]]]&] (* Harvey P. Dale, Feb 06 2020 *)

PARI

forprime(p=1,1999,isprime(p+sumdigits(p,4))&&print1(p","))