This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A233580 In balanced ternary notation, zerofree non-repdigit numbers that are either palindromes or sign reversed palindromes. 1


%S 2,7,16,20,32,43,61,103,124,146,182,196,292,302,338,367,421,547,601,

%T 859,913,1039,1096,1172,1280,1312,1600,1640,1748,1816,2560,2624,2732,

%U 2776,3064,3092,3200,3283,3445,3823,3985,4759,4921,5299,5461,7663,7825,8203

%N In balanced ternary notation, zerofree non-repdigit numbers that are either palindromes or sign reversed palindromes.

%C Zerofree numbers in balanced ternary notation can be used as reversible sign operators. This sequence collects such operators that are either in palindrome form or sign reversed palindrome form (which is defined as (n)_bt+Reverse((n)_bt)=0).

%H Lei Zhou, <a href="/A233580/b233580.txt">Table of n, a(n) for n = 1..10000</a>

%e 2 = (1T)_bt in balanced ternary notation, where we use T to represent -1.

%e 1T + T1 = 0, matches the definition of sign reversed palindrome form. So 2 is in the sequence.

%e Other examples:

%e 7 = (1T1_bt) - palindrome; in the sequence.

%e 13 = (111)_bt - palindrome but repdigit; not in the sequence.

%e 16 = (1TT1)_bt - palindrome; in the sequence.

%e ...

%e 52 = (1T0T1)_bt - palindrome but not zerofree; not in the sequence.

%t BTDigits[m_Integer, g_] :=

%t (* This is to determine digits of a number in balanced ternary notation. *)

%t Module[{n = m, d, sign, t = g}, If[n != 0, If[n > 0, sign = 1,

%t sign = -1; n = -n]; d = Ceiling[Log[3, n]]; If[3^d - n <= ((3^d - 1)/2), d++]; While[Length[t] < d, PrependTo[t, 0]]; t[[Length[t] + 1 - d]] = sign; t = BTDigits[sign*(n - 3^(d - 1)), t]]; t];

%t BTnum[g_]:=Module[{bo=Reverse[g],data=0,i},Do[data=data+3^(i-1)*bo[[i]],{i,1,Length[bo]}];data];

%t ct=0;n=0;dg=0;spool={};res={};While[ct<50,n++; nbits = BTDigits[n, {0}];cdg=Length[nbits];If[cdg>dg,If[Length[spool]>0,Do[bits=spool[[j]];If[!MemberQ[bits,0],rb=Reverse[bits]; sign=rb[[1]];bo=Join[bits,-sign*rb];If[MemberQ[bo,-1],data=BTnum[bo];ct++;AppendTo[res,data]];bo=Join[bits,sign*rb];If[MemberQ[bo,-1],data=BTnum[bo];ct++;AppendTo[res,data]]],{j,1,Length[spool]}];Do[bits=spool[[j]];If[!MemberQ[bits,0],rb=Reverse[bits];bo=Join[bits,{-1},rb];If[MemberQ[bo,-1],data=BTnum[bo];ct++;AppendTo[res,data]];bo=Join[bits,{1},rb];If[MemberQ[bo,-1],data=BTnum[bo];ct++;AppendTo[res,data]]],{j,1,Length[spool]}];spool={};dg=cdg]];AppendTo[spool,nbits]];Print[res]

%Y Cf. A002113, A061917, A006995, A057890, A134027, A233010, A233571, A233572.

%K nonn,base,easy

%O 1,1

%A _Lei Zhou_, Dec 14 2013

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)