The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101703 Numbers n such that reversal(n) = (2/3)*n - 2. 3

%I #15 Jun 21 2015 14:26:46

%S 21,291,885,2991,29991,234651,299991,2340651,2999991,8221845,23400651,

%T 29346591,29999991,234000651,293406591,299999991,2340000651,

%U 2346534651,2934006591,2993465991,2999999991,23400000651,23465934651,29340006591,29934065991,29999999991,82277815845,234000000651

%N Numbers n such that reversal(n) = (2/3)*n - 2.

%C Numbers of the form 3*(10^n-3) are in the sequence, so A086947 is an infinite subsequence of this sequence. Also A101700 is a subsequence of this sequence.

%C Let f(r,s,t,z) = 2.(9)(r+s).(34.(0)(t).65)(z).(9)(s).1 where the dot between numbers means concatenation and "(m)(n)" means number of m's is n, for example f(0,2,1,3)= 299340653406534065991, it is interesting that all numbers of the form f(r,s,t,z) where r, s, t & z are nonnegative integers and r*z=0 are in this sequence.

%C Except for 885 & 8221845 all known terms of this sequence are of the form f(r,s,t,z).

%C For all r, s & t we have f(r,s,t,0)=f(r,s,0,0)=f(r+2s,0,0,0)=A086947(r+2s+1)= 3*(10^(r+2s+1)-3).

%C a(1) = 21 = f(0,0,0,0), a(2) = 291 = f(1,0,0,0), a(4) = 2991 = f(2,0,0,0) = f(0,1,0,0), a(5) = 29991 = f(3,0,0,0) = f(1,1,0,0), a(6) = 234651 = f(0,0,0,1), a(7) = 299991 = f(4,0,0,0) = f(0,2,0,0), a(8) = 2340651 = f(0,0,1,1), etc. Next term is greater than 11*10^8.

%C From _David Wasserman_, Mar 27 2008: (Start)

%C 234653406534651 is a term that doesn't fit the f(r,s,t,z) format.

%C We may redefine f so that t is a vector of length z, which must be symmetrical to produce a member. For example f(0,0,[0,1,0],3) = 234653406534651 is a member, but f(0,0,[1,0,0],3) = 234065346534651 is not a member.

%C 23465934651 is another member that doesn't fit the pattern. In general there may be any number of 9's between a 5 and a 3, provided that the 9's are symmetrical. So 2346593465934651 is a member, but 23465993465934651 is not. (End)

%H Giovanni Resta, <a href="/A101703/b101703.txt">Table of n, a(n) for n = 1..56</a> (terms < 10^14)

%e f(0,1,2,3) = 2934006534006534006591 is in the sequence because reversal(2934006534006534006591) = 1956004356004356004392 = (2/3)*2934006534006534006591-2.

%t Do[If[FromDigits[Reverse[IntegerDigits[n]]] == 2/3*n - 2, Print[n]], {n, 1100000000}]

%Y Cf. A086947, A069215, A101700, A101704.

%K base,nonn

%O 1,1

%A _Farideh Firoozbakht_, Dec 31 2004

%E More terms from _David Wasserman_, Mar 27 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 9 18:00 EDT 2024. Contains 373248 sequences. (Running on oeis4.)