A295520 a(n) is the least k >= 0 such that n XOR k is prime (where XOR denotes the bitwise XOR operator).

2, 2, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 3, 2, 1, 0, 5, 4, 5, 4, 1, 0, 1, 0, 5, 4, 7, 6, 1, 0, 3, 2, 1, 0, 1, 0, 3, 2, 1, 0, 5, 4, 7, 6, 1, 0, 3, 2, 3, 2, 1, 0, 1, 0, 3, 2, 3, 2, 1, 0, 3, 2, 1, 0, 1, 0, 3, 2, 3, 2, 1, 0, 3, 2, 1, 0, 7, 6, 5

Offset

0,1

Comments

a(n) = n iff n is prime.

For any n >= 0, a(n) <= A295335(n).

See A295335 for the OR variant.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Rémy Sigrist, Scatterplot of (x, y) such that x XOR y is prime and x, y < 1024

Formula

Empirically, for any k > 1, a(2*k+1) = a(2*k)-1.

Example

For n = 44:
- 44 XOR 0 = 44 is not prime,
- 44 XOR 1 = 45 is not prime,
- 44 XOR 2 = 46 is not prime,
- 44 XOR 3 = 47 is prime,
- hence a(44) = 3.

Maple

f:= proc(n) local k;
  for k from 0 do if isprime(Bits:-Xor(k, n)) then return k fi od
end proc:
map(f, [$0..200]); # Robert Israel, Nov 27 2017

Mathematica

Table[Block[{k = 0}, While[! PrimeQ@ BitXor[k, n], k++]; k], {n, 0, 104}] (* Michael De Vlieger, Nov 26 2017 *)

Prog

(PARI) a(n) = for (k=0, oo, if (isprime(bitxor(n, k)), return (k)))
(Python)
from itertools import count
from sympy import isprime
def A295520(n): return next(k for k in count(0) if isprime(n^k)) # Chai Wah Wu, Aug 23 2023

Crossrefs

Cf. A295335.

Sequence in context: A297814 A298177 A298146 * A295335 A227838 A050605

Adjacent sequences: A295517 A295518 A295519 * A295521 A295522 A295523

Keyword

nonn,base

Author

Rémy Sigrist, Nov 23 2017

Status

approved