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A293983 a(n) = least k > 0 such that prime(k) XOR prime(k+1) XOR ... XOR prime(A293927(n)) = 0 (where XOR denotes the binary XOR operator, and prime(n) = A000040(n)).

%I A293983 #14 Jul 12 2019 17:07:15
%S A293983 8,19,15,26,33,30,26,38,22,49,47,45,58,63,69,63,65,65,71,69,69,92,92,
%T A293983 88,123,86,123,80,132,140,80,70,153,161,56,155,176,182,145,195,143,
%U A293983 185,133,202,125,123,216,225,235,121,237,246,235,219,227,105,260,254
%N A293983 a(n) = least k > 0 such that prime(k) XOR prime(k+1) XOR ... XOR prime(A293927(n)) = 0 (where XOR denotes the binary XOR operator, and prime(n) = A000040(n)).
%C A293983 If a(n) = 1, then A126084(A293927(n)) = 0.
%C A293983 For any n > 0, A293927(n) - a(n) + 1 >= 4 (we need to XOR at least 4 consecutive prime numbers in order to obtain 0).
%C A293983 For any n > 0, if a(n) > 1 then A293927(n) - a(n) + 1 is even (we need to XOR an even number of odd prime numbers in order to obtain 0).
%H A293983 Rémy Sigrist, <a href="/A293983/b293983.txt">Table of n, a(n) for n = 1..10000</a>
%o A293983 (PARI) prev = vector(1774); s = 0; pi = 0; n = 0; forprime (p=1, 1697, pi++; s = bitxor(s, p); if (s==0 || prev[s], n++; print1 (prev[s]+1 ", "), prev[s] = pi));
%Y A293983 Cf. A000040, A126084, A293927.
%K A293983 nonn,base
%O A293983 1,1
%A A293983 _Rémy Sigrist_, Oct 21 2017