A080679 Lexicographically earliest de Bruijn cycle of length 16 (repeated indefinitely).

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

Offset

0,1

References

N. G. de Bruijn, A combinatorial problem, Koninklijke Nederlandse Akademie v. Wetenschappen 49, 758-764, 1946.

S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967, Chap. VI, Section 2.2.

Links

Table of n, a(n) for n=0..98.

Alex Bogomolny, Lewis Carroll to Archimedes

F. R. K. Chung, P. Diaconis and R. L. Graham, Universal cycles for combinatorial structures, Discr. Math., 110 (1992), 43-59.

Frank Ruskey, Generate Necklaces

Index entries for periodic sequences.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

a(n) = (1/240)*{16*(n mod 16)+[(n+1) mod 16]+[(n+2) mod 16]+[(n+3) mod 16]-14*[(n+4) mod 16]+16*[(n+5) mod 16]-14*[(n+6) mod 16]+16*[(n+7) mod 16]+[(n+8) mod 16]-14*[(n+9) mod 16]+[(n+10) mod 16]+16*[(n+11) mod 16]-14*[(n+12) mod 16]+[(n+13) mod 16]+[(n+14) mod 16]+[(n+15) mod 16]}.

Periodic with period 16.

Example

The period is 0000100110101111.

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1}, 99] (* Ray Chandler, Aug 26 2015 *)
PadRight[{}, 120, {0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1}] (* Harvey P. Dale, Dec 27 2025 *)

Prog

(PARI) a(n)=[0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1][n%16+1] \\ Charles R Greathouse IV, May 12 2026
(PARI) a(n)=bittest(62864, n%16) \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A169671, A169672, A169673, A169674.

Sequence in context: A011664 A179831 A094091 * A353464 A144193 A171387

Adjacent sequences: A080676 A080677 A080678 * A080680 A080681 A080682

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 03 2003

Status

approved