A196657 a(n) = 63*2^(n+1) + 1.

127, 253, 505, 1009, 2017, 4033, 8065, 16129, 32257, 64513, 129025, 258049, 516097, 1032193, 2064385, 4128769, 8257537, 16515073, 33030145, 66060289, 132120577, 264241153, 528482305, 1056964609, 2113929217, 4227858433, 8455716865, 16911433729, 33822867457

Offset

0,1

Comments

Binary numbers of form 111111(n)1 where n is the index and number of 0's.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

From Elmo R. Oliveira, Dec 01 2025: (Start)

G.f.: (127-128*x)/((2*x-1)*(x-1)).

E.g.f.: exp(x)*(1 + 126*exp(x)).

a(n) = 3*a(n-1) - 2*a(n-2). (End)

Example

First few terms in binary are 1111111, 11111101, 111111001, 1111110001, 11111100001.

Mathematica

LinearRecurrence[{3, -2}, {127, 253}, 50] (* Vincenzo Librandi, Nov 25 2011 *)

Prog

(Magma) [63*2^(n+1) + 1: n in [0..100]];
(PARI) a(n)=126<<n+1 \\ Charles R Greathouse IV, Oct 06 2011

Crossrefs

Cf. A196658 (subsequence of primes).

Sequence in context: A142551 A048453 A276495 * A138127 A157949 A142165

Adjacent sequences: A196654 A196655 A196656 * A196658 A196659 A196660

Keyword

nonn,easy

Author

Brad Clardy, Oct 04 2011

Status

approved