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
Offset: 1
Examples
a(3) = 101*109989 - 100*1089 = 10999989.
Links
- 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).
Programs
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Magma
[11*(10^(2*n) - 1): n in [1..20]];
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Maple
A274755:= n-> 11*(10^(2*n) - 1) : seq(A274755(n), n=1..20);
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Mathematica
Array[99(10^(2 #)- 1)/9&, 15] LinearRecurrence[{101, -100}, {1089, 109989}, 20] (* Vincenzo Librandi, Jul 07 2016 *) -
PARI
Vec(1089*x/((1-x)*(1-100*x)) + O(x^99)) \\ Altug Alkan, Jul 06 2016
Formula
a(n) = 101*a(n-1) - 100*a(n-2), with a(1)= 1089 and a(2)= 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
E.g.f.: 11*exp(x)*(exp(99*x) - 1). - Elmo R. Oliveira, Jun 09 2025
Comments