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%I #16 Dec 03 2019 05:12:23
%S 2,1,4,2,1,1,3,4,2,1,1,2,1,1,3,8,2,1,4,2,1,1,1,4,2,1,1,2,1,1,3,16,2,1,
%T 4,2,1,1,3,4,2,1,1,2,1,1,1,8,2,1,4,2,1,1,1,4,2,1,1,2,1,1,3,32,2,1,4,2,
%U 1,1,3,4,2,1,1,2,1,1,3,8,2,1,4,2,1,1
%N Least positive integer k such that A014577(k - 1) != A014577(n + k - 1).
%C a(2n) = A006519(n) and a(2n+1) = b(n), where (b(n))_{n >= 0} is a 2-automatic sequence defined by applying the coding tau(01234) = 24131 to the fixed point of the morphism defined by 0 -> 01, 1 -> 23, 2 -> 04, 3 -> 23, 4 -> 24.
%H Peter Luschny, <a href="/A330086/b330086.txt">Table of n, a(n) for n = 1..1000</a>
%p with(ListTools): with(numtheory):
%p J := (n, k) -> jacobi(-1, k) <> jacobi(-1, n+k):
%p a := n -> SelectFirst(k -> J(n, k), [seq(k, k=1..100000)]):
%p seq(a(n), n=1..86); # _Peter Luschny_, Dec 02 2019
%t Block[{nn = 86, s}, s = Array[Boole[EvenQ[((# + 1)/2^IntegerExponent[# + 1, 2] - 1)/2]] &, 3 nn, 0]; Array[Block[{i = 1}, While[s[[i]] == s[[# + i]], i++]; i] &, nn]] (* _Michael De Vlieger_, Dec 01 2019 *)
%Y Cf. A014577, A006519.
%K nonn
%O 1,1
%A _Jeffrey Shallit_, Dec 01 2019
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