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

0,3

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

Links

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

Formula

a(9*n) = n.

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A375481 A023125 A319657 * A030108 A307651 A297330

Adjacent sequences: A255591 A255592 A255593 * A255595 A255596 A255597

Keyword

nonn,easy,base

Author

Paolo P. Lava, Mar 02 2015

Status

approved