A255594 - OEIS

%I #32 Jun 14 2024 19:19:10

%S 0,1,2,3,4,5,6,7,8,1,10,19,28,37,46,55,64,73,2,11,20,29,38,47,56,65,

%T 74,3,12,21,30,39,48,57,66,75,4,13,22,31,40,49,58,67,76,5,14,23,32,41,

%U 50,59,68,77,6,15,24,33,42,51,60,69,78,7,16,25,34,43,52,61

%N Convert n to base 9, move least significant digit to most significant digit and convert back to base 10.

%C Fixed points of the transform are listed in A048334.

%C For more than 2 base-9 digits, reversal and cyclic shifts of a number start to differ, so this sequence differs from A030108. - _Alonso del Arte_, Mar 22 2015

%H Paolo P. Lava, <a href="/A255594/b255594.txt">Table of n, a(n) for n = 0..1000</a>

%F a(9*n) = n.

%F a(9^n) = 9^(n-1).

%e 13 in base 9 is 14: moving the least significant digit as the most significant one we have 41 that is 37 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(10^4,9);

%t roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 9; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* _Michael De Vlieger_, Mar 04 2015 *)

%t Table[FromDigits[RotateRight[IntegerDigits[n,9]],9],{n,0,80}] (* _Harvey P. Dale_, Jun 14 2024 *)

%Y Cf. A030108, A038572, A048334, A255588-A255593, A048787, A255689-A255693.

%K nonn,easy,base

%O 0,3

%A _Paolo P. Lava_, Mar 02 2015