A346408 Primes whose bitwise XOR of decimal digits is a prime.

2, 3, 5, 7, 13, 29, 31, 41, 43, 47, 61, 83, 103, 113, 131, 137, 139, 151, 157, 173, 193, 211, 223, 227, 233, 241, 263, 269, 277, 281, 311, 317, 337, 353, 367, 373, 379, 389, 397, 401, 409, 421, 443, 461, 467, 487, 557, 571, 577, 599, 601, 641, 647, 673, 683

Offset: 1

Author

Jeremias M. Gomes, Jul 21 2021

Keywords

• base
• nonn
• less

Examples

			421 is a term because it is a prime whose bitwise XOR of digits is 7 which is also a prime.
		

Links

• Wikipedia, Bitwise operation

Crossrefs

Cf. A000040, A346511 (XOR of digits of n).

Programs

Maple

b:= l-> `if`(l=[], 0, Bits[Xor](l[1], b(subsop(1=[][], l)))):
q:= n-> isprime(b(convert(n, base, 10))):
select(q, [ithprime(i)$i=1..160])[];  # Alois P. Heinz, Jul 21 2021

Mathematica

Select[Range[1000], PrimeQ[#] && PrimeQ[BitXor @@ IntegerDigits[#]] &] (* Amiram Eldar, Jul 21 2021 *)

Sage

def XOR(a, b):
    return a ^^ b
[n for n in (0..100) if (n in Primes() and reduce(XOR, map(lambda x: int(x), str(n))) in Primes())]