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A181359 a(1)=1. After that, a(n) = a(n-1) XOR a(floor(sqrt(n))). 1

%I #17 Sep 08 2022 08:45:54

%S 1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,

%T 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,

%U 0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0

%N a(1)=1. After that, a(n) = a(n-1) XOR a(floor(sqrt(n))).

%H Antti Karttunen, <a href="/A181359/b181359.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(1) = 1; for n > 1, a(n) = A000035(a(n-1) + a(A000196(n))). - _Antti Karttunen_, Dec 16 2017, after Magma program of _Klaus Brockhaus_

%t f[1] := True

%t f[x_] := Xor[f[x - 1], f[Floor[Sqrt[x]]]]

%o (Magma) [ n eq 1 select 1 else (Self(n-1)+Self(Isqrt(n))) mod 2: n in [1..105] ]; // _Klaus Brockhaus_, Oct 16 2010

%o (PARI) first(n) = my(res = vector(n)); res[1]=1; for(x=2, n, res[x]=bitxor(res[x-1], res[floor(sqrt(x))])); res \\ _Iain Fox_, Dec 16 2017

%o (Scheme, with memoization-macro definec) (definec (A181359 n) (if (= 1 n) n (A000035 (+ (A181359 (- n 1)) (A181359 (A000196 n)))))) ;; _Antti Karttunen_, Dec 16 2017

%Y Cf. A000196 (integer part of square root of n). - _Klaus Brockhaus_, Oct 16 2010

%K nonn

%O 1,1

%A _Ben Branman_, Oct 14 2010

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)