A274743 Repunits with odd indices multiplied by 99, i.e., 99*(1, 111, 11111, 1111111, ...).

99, 10989, 1099989, 109999989, 10999999989, 1099999999989, 109999999999989, 10999999999999989, 1099999999999999989, 109999999999999999989, 10999999999999999999989, 1099999999999999999999989, 109999999999999999999999989, 10999999999999999999999999989

Offset

1,1

Comments

It is apparent that the reciprocals of the terms in the sequence give an increasing sequence of periodic terms similar to A095372, but with the initial term equal to "01". The leading zero is important (see links). Furthermore, the reciprocals of the terms give a sequence of even growing periods, starting from 2, with delta = 4 (i.e., 2, 6, 10, 14, 18, ...).

Adding "11" to each term gives the binary representation of the n-th iteration of "Rule 14" elementary cellular automaton starting with a single ON (black cell) as in A266299.

Links

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

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

Rodolfo 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

G.f.: 99*x*(1 + 10*x)/((1 - x)*(1 - 100*x)). - Ilya Gutkovskiy, Jul 04 2016

a(n) = 101*a(n-1) - 100*a(n-2) for n>2, with a(0)= 99 and a(1)= 10989.

a(n) = 99*A100706(n-1).

a(n) = 11*(10^(2*n-1)-1). - Wesley Ivan Hurt, Jul 04 2016

Example

a(2) = 101*10989 - 100*99 = 1099989.

Maple

A274743:=n->11*(10^(2*n-1)-1): seq(A274743(n), n=1..20); # Wesley Ivan Hurt, Jul 04 2016

Mathematica

Array[99(10^(2 # - 1) - 1)/9 &, 15] (* Michael De Vlieger, Jul 04 2016 *)
99*Table[FromDigits[PadRight[{}, 2n+1, 1]], {n, 0, 15}] (* Harvey P. Dale, Jul 22 2019 *)

Prog

(Magma) [11*(10^(2*n-1)-1) : n in [1..20]]; // Wesley Ivan Hurt, Jul 04 2016
(PARI) Vec(99*x*(1+10*x)/((1-x)*(1-100*x)) + O(x^99)) \\ Altug Alkan, Jul 05 2016
(PARI) a002275(n) = (10^n-1)/9
a(n) = 99*a002275(2*n-1) \\ Felix Fröhlich, Jul 05 2016

Crossrefs

Cf. A002275, A095372, A100706, A266299, A274755.

Sequence in context: A327926 A098609 A195623 * A244842 A190921 A213694

Adjacent sequences: A274740 A274741 A274742 * A274744 A274745 A274746

Keyword

nonn,easy

Author

Rodolfo A. Fiorini, Jul 04 2016

Status

approved