A274755 - OEIS

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A274755

Repunits with even indices multiplied by 99, i.e., 99*(11, 1111, 111111, 11111111, ...).

1089, 109989, 10999989, 1099999989, 109999999989, 10999999999989, 1099999999999989, 109999999999999989, 10999999999999999989, 1099999999999999999989, 109999999999999999999989, 10999999999999999999999989, 1099999999999999999999999989

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The reciprocals of the terms give a sequence of even growing periods, starting from 22, with delta = 22 (i.e., 22,44,66,88,110,132,...).

LINKS

Table of n, a(n) for n=1..13.

R. A. Fiorini, How Random is Your Tomographic Noise? A Number Theoretic Transform (NTT) Approach, Fundamenta Informaticae, 135(1-2), 2014, 135-170.

R. A. Fiorini, Computerized tomography noise reduction by CICT optimized exponential cyclic sequences (OECS) co-domain, Fundamenta Informaticae, vol.141 (2015), 115-134.

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

FORMULA

a(n) = 101*a(n-1) - 100*a(n-2), with a(0)= 1089 and a(1)= 109989.

G.f.: 1089*x/((1 - x)*(1 - 100*x)). - Ilya Gutkovskiy, Jul 04 2016

a(n) = 99*A099814(n). - Michel Marcus, Jul 04 2016

a(n) = 11*(10^(2*n)-1). - Robert Israel, Jul 06 2016

EXAMPLE

a(2) = 101*109989 - 100*1089 = 10999989.

MAPLE

A274755:= n-> 11*(10^(2*n) - 1) : seq(A274755(n), n=1..20);

MATHEMATICA

Array[99(10^(2 #)- 1)/9&, 15]

LinearRecurrence[{101, -100}, {1089, 109989}, 20] (* Vincenzo Librandi, Jul 07 2016 *)

PROG

(Magma) [11*(10^(2*n) - 1): n in [1..20]]:

(PARI) Vec(1089*x/((1-x)*(1-100*x)) + O(x^99)) \\ Altug Alkan, Jul 06 2016

CROSSREFS

Cf. A002275, A099814, A274743.

Sequence in context: A001232 A039684 A230066 * A023101 A169977 A345408

Adjacent sequences: A274752 A274753 A274754 * A274756 A274757 A274758

KEYWORD

nonn,easy

AUTHOR

Rodolfo A. Fiorini, Jul 04 2016

STATUS

approved