A255594 Convert n to base 9, move least significant digit to most significant digit and convert back to base 10.

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, 74, 3, 12, 21, 30, 39, 48, 57, 66, 75, 4, 13, 22, 31, 40, 49, 58, 67, 76, 5, 14, 23, 32, 41, 50, 59, 68, 77, 6, 15, 24, 33, 42, 51, 60, 69, 78, 7, 16, 25, 34, 43, 52, 61

Offset: 0

Author

Paolo P. Lava, Mar 02 2015

Keywords

• nonn
• easy
• base

Comments

Fixed points of the transform are listed in A048334.

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

Examples

			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.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 0..1000

Crossrefs

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

Programs

Maple

with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
for n from 1 to q do
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]];
a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;
print(b); od; end: P(10^4,9);

Mathematica

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 *)
Table[FromDigits[RotateRight[IntegerDigits[n,9]],9],{n,0,80}] (* Harvey P. Dale, Jun 14 2024 *)

Formula

a(9*n) = n.

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