|
%I #36 May 13 2023 13:25:53
%S 0,1,2,1,4,7,2,5,8,3,12,21,4,13,22,5,14,23,6,15,24,7,16,25,8,17,26,9,
%T 36,63,10,37,64,11,38,65,12,39,66,13,40,67,14,41,68,15,42,69,16,43,70,
%U 17,44,71,18,45,72,19,46,73,20,47,74,21,48,75,22,49,76,23
%N Convert n to base 3, move the least significant digit to the most significant one and convert back to base 10.
%C a(3*n) = n.
%C Fixed points of the transform are listed in A048328.
%H Indranil Ghosh, <a href="/A255588/b255588.txt">Table of n, a(n) for n = 0..19683</a> (terms 0..1000 Paolo P. Lava)
%e 10 in base 3 is 101: moving the least significant digit to the most significant one we have 110 that is 12 in base 10.
%p with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
%p for n from 1 to q do
%p a:=convert(n,base,h); b:=[]; for k from 2 to nops(a) do b:=[op(b),a[k]]; od; a:=[op(b),a[1]];
%p a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
%p print(b); od; end: P(10^4,3);
%t roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 3; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* _Michael De Vlieger_, Mar 04 2015 *)
%t Table[FromDigits[RotateRight[IntegerDigits[n,3]],3],{n,0,70}] (* _Harvey P. Dale_, Feb 20 2022 *)
%o (Python)
%o def A255588(n):
%o x=A007089(n)
%o return int(x[-1]+x[:-1], 3) # _Indranil Ghosh_, Feb 03 2017
%Y Cf. A030102, A038572, A048328, A255589-A255594, A048787, A255689-A255693.
%K nonn,easy,base
%O 0,3
%A _Paolo P. Lava_, Feb 27 2015
|
