A293927 Numbers n such that prime(k) XOR prime(k+1) XOR ... XOR prime(n) = 0 for some k < n (where XOR denotes the binary XOR operator, and prime(n) = A000040(n)).

17, 28, 30, 33, 36, 43, 45, 47, 51, 52, 56, 58, 65, 66, 72, 74, 76, 80, 84, 90, 94, 107, 111, 119, 126, 129, 130, 133, 137, 143, 145, 155, 156, 166, 169, 174, 179, 185, 192, 200, 202, 204, 208, 213, 214, 216, 219, 228, 238, 246, 248, 249, 250, 254, 258, 262

Offset: 1

Author

Rémy Sigrist, Oct 21 2017

Keywords

• nonn
• base

Comments

Equivalently, numbers n such that A126084(n) = A126084(m) for some m < n.

See A293983(n) for the least k such that prime(k) XOR prime(k+1) XOR ... XOR prime(a(n)) = 0.

Examples

			prime(33) XOR prime(34) XOR prime(35) XOR prime(36) = 137 XOR 139 XOR 149 XOR 151 = 0, hence 36 appears in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A126084, A293983.

Programs

Maple

N:= 1000: # to get all terms <= N
R[0]:= 0: T:= 2: p:= 2;
Res:= NULL:
for n from 2 to N do
  p:= nextprime(p);
  T:= Bits:-Xor(T,p);
  if assigned(R[T]) then Res:= Res, n
  else R[T]:= n
  fi
od:
Res; # Robert Israel, Oct 22 2017

PARI

s = 0; seen = 2^0; for (i = 1, 262, s = bitxor(s, prime(i)); if (bittest(seen, s), print1 (i ", "), seen += 2^s))