A181359 - OEIS

A181359

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

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, 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, 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

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OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

FORMULA

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

MATHEMATICA

f[1] := True

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

PROG

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

(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

(Scheme, with memoization-macro definec) (definec (A181359 n) (if (= 1 n) n (A000035 (+ (A181359 (- n 1)) (A181359 (A000196 n)))))) ;; Antti Karttunen, Dec 16 2017

CROSSREFS

Cf. A000196 (integer part of square root of n). - Klaus Brockhaus, Oct 16 2010

Sequence in context: A254377 A285657 A162519 * A072418 A128973 A176412

Adjacent sequences: A181356 A181357 A181358 * A181360 A181361 A181362

KEYWORD

nonn

AUTHOR

Ben Branman, Oct 14 2010

STATUS

approved