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

Author

Farideh Firoozbakht, Dec 31 2004

Keywords

• base
• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A101703, A101705.

Programs

Mathematica

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

Extensions

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