A101703 -id:A101703 - cp's OEIS frontend

A101704 Numbers n such that reversal(n)=2n/3.

0, 6534, 65934, 659934, 6599934, 65346534, 65999934, 653406534, 659999934, 6534006534, 6593465934, 6599999934, 65340006534, 65934065934, 65999999934, 653400006534, 653465346534, 659340065934, 659934659934, 659999999934, 6534000006534, 6534659346534, 6593400065934, 6599340659934, 6599999999934

Offset: 1

Farideh Firoozbakht, Dec 31 2004

If n=0 or n>1 then 66*(10^n-1) is in the sequence (the first five terms of this sequence are of this form) so this sequence is infinite. Let g(s,t,r) be (s.(0)(t))(r).s where dot between numbers means concatenation and "(m)(n)" means number of m's is n, for example g(2005,1,2)=20050200502005. It is interesting that, if n is in the sequence then all numbers of the form g(n,t,r) for nonnegative integers t and r are in the sequence, for example since 6534 is in the sequence so g(6534,1,2)=(6534.(0)(1))(2).6534=65340653406534 is in the sequence.
It seems that all similar sequences (sequences with the definition "numbers n such that reversal(n) =r*n for a fixed rational number r" ) have the same property (see A101705 and A101706). All sequences of the form 10^s*A002113 are in this category.
There are Fibonacci(floor((n-2)/2)) terms with n digits, n>1 (this is essentially A103609). - Ray Chandler, Oct 12 2017

			g(65934,3,4)=6593400065934000659340006593400065934 is in the sequence
because reversal(6593400065934000659340006593400065934)
= 4395600043956000439560004395600043956
=2/3*6593400065934000659340006593400065934.

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A101703, A101705.

Do[If[FromDigits[Reverse[IntegerDigits[n]]] == 2/3*n, Print[n]], {n, 150000000}]

a(8)-a(25) from Max Alekseyev, Aug 18 2013

A086947 Numbers k such that R(k+9) = 3.

Original entry on oeis.org

21, 291, 2991, 29991, 299991, 2999991, 29999991, 299999991, 2999999991, 29999999991, 299999999991, 2999999999991, 29999999999991, 299999999999991, 2999999999999991, 29999999999999991, 299999999999999991, 2999999999999999991, 29999999999999999991, 299999999999999999991

Offset: 1

Ray Chandler, Jul 24 2003

If k is in this sequence then Reverse(k) = (2/3)*k - 2. Also A101703 is the sequence of all numbers k such that Reverse(k) = (2/3)*k - 2. So this sequence is a subsequence of A101703. - Farideh Firoozbakht, Dec 30 2004

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A004086, A085331, A086948, A101700, A101703, A173833.

[3*(10^n-3): n in [1..25] ]; // Vincenzo Librandi, Aug 22 2011

Table[3*(10^n-3), {n, 17}]
Table[FromDigits[PadRight[{3},n,0]],{n,2,20}]-9 (* Harvey P. Dale, Nov 27 2012 *)

a(n) = 3*(10^n - 3).
R(a(n)) = A086948(n).
From Chai Wah Wu, Aug 01 2020: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2.
G.f.: x*(60*x + 21)/((x - 1)*(10*x - 1)). (End)
From Elmo R. Oliveira, May 01 2025: (Start)
E.g.f.: 3*(2 - 3*exp(x) + exp(10*x)).
a(n) = 3*A173833(n). (End)

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A101704 Numbers n such that reversal(n)=2n/3.

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