1,2

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. Next term is greater than 150000000.

g(65934,3,4)=6593400065934000659340006593400065934 is in the sequence

because reversal(6593400065934000659340006593400065934)

= 4395600043956000439560004395600043956

=2/3*6593400065934000659340006593400065934.

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

Cf. A101703, A101705.

Sequence in context: A049529 A068270 A034627 this_sequence A043488 A046321 A043456

Adjacent sequences: A101701 A101702 A101703 this_sequence A101705 A101706 A101707

base,more,nonn

Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Dec 31 2004