A176067 Binary analog of A098755 and A098756: Binary representation of least available nonnegative integer with bit values alternating for entire sequence.

1, 0, 10, 1010, 101010, 10101010, 1010101010, 101010101010, 10101010101010, 1010101010101010, 101010101010101010, 10101010101010101010, 1010101010101010101010, 101010101010101010101010, 10101010101010101010101010, 1010101010101010101010101010

Offset

-1,3

Comments

Begin at a(-1) = 1 for A098756 analog; begin at a(0) = 0 for A098755 analog. A020988 gives the corresponding decimal representations for n >= 0; see relevant comments there and in A163662: This sequence is A163662 with 1, 0 prefixed.

Links

Table of n, a(n) for n=-1..14.

Index entries for linear recurrences with constant coefficients, signature (101, -100).

Formula

a(n) = A007088(A020988(n)) for n >= 0; a(-1) = 1.

From Chai Wah Wu, Feb 11 2018: (Start)

a(n) = 101*a(n-1) - 100*a(n-2) for n > 1.

G.f.: (110*x^2 - 101*x + 1)/(x*(x - 1)*(100*x - 1)). (End)

Mathematica

Join[{1, 0}, RecurrenceTable[{a[1]==10, a[2]==1010, a[n]==101 a[n-1] - 100 a[n-2]}, a, {n, 15}]] (* Vincenzo Librandi, Feb 11 2018 *)

Prog

(Magma)   I:=[1, 0, 10]; [n le 3 select I[n] else 101*Self(n-1)-100*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 11 2018

Crossrefs

Cf. A098755, A098756, A020988, A007088, A163662.

Sequence in context: A106456 A079214 A163662 * A080070 A303610 A080120

Adjacent sequences: A176064 A176065 A176066 * A176068 A176069 A176070

Keyword

base,easy,nonn

Author

Rick L. Shepherd, Apr 07 2010

Status

approved