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