A392742 - OEIS

A392742

A 4-automatic binary sequence with irreducible nested recurrence (see Comments).

0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1

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OFFSET

COMMENTS

The selector 2n+a(n) is the "twin" of 2n+1-a(n) used in A392736. The sequence is balanced and 4-automatic with a DFAO with 4 states.

LINKS

Table of n, a(n) for n=0..79.

FORMULA

a(n) is defined by a(0)=0, a(1)=1, and for n>=0: a(4n) = a(n), a(4n+1) = 1-a(n), a(4n+2) = a(2n+a(n)), a(4n+3) = 1-a(2n+a(n)).

EXAMPLE

For n=2: a(4*2+2) = a(10) = a(2*2+a(2)) = a(4+0) = a(4) = 1.

MATHEMATICA

a[0] = 0; a[1] = 1; a[n_] := a[n] = Which[Mod[n, 4] == 0, a[Quotient[n, 4]], Mod[n, 4] == 1, 1 - a[Quotient[n, 4]], Mod[n, 4] == 2, a[2*Quotient[n, 4] + a[Quotient[n, 4]]], True, 1 - a[2*Quotient[n, 4] + a[Quotient[n, 4]]]]; Table[a[n], {n, 0, 79}]

PROG

(PARI) a(n) = if(n<2, n, my(q=n\4, r=n%4); if(r==0, a(q), r==1, 1-a(q), r==2, a(2*q+a(q)), 1-a(2*q+a(q))));

CROSSREFS

Cf. A392736, A010060 (Thue-Morse).

Sequence in context: A165211 A341389 A188027 * A359333 A193496 A379798

Adjacent sequences: A392739 A392740 A392741 * A392743 A392744 A392745

KEYWORD

nonn,easy

AUTHOR

John M. Campbell and Benoit Cloitre, Jan 21 2026

STATUS

approved