A255588 Convert n to base 3, move the least significant digit to the most significant one and convert back to base 10.

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, 36, 63, 10, 37, 64, 11, 38, 65, 12, 39, 66, 13, 40, 67, 14, 41, 68, 15, 42, 69, 16, 43, 70, 17, 44, 71, 18, 45, 72, 19, 46, 73, 20, 47, 74, 21, 48, 75, 22, 49, 76, 23

Offset: 0

Author

Paolo P. Lava, Feb 27 2015

Keywords

• nonn
• easy
• base

Comments

a(3*n) = n.

Fixed points of the transform are listed in A048328.

Examples

			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.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..19683 (terms 0..1000 Paolo P. Lava)

Crossrefs

Cf. A030102, A038572, A048328, A255589-A255594, 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(10^4,3);

Mathematica

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 *)
Table[FromDigits[RotateRight[IntegerDigits[n,3]],3],{n,0,70}] (* Harvey P. Dale, Feb 20 2022 *)

Python

def A255588(n):
    x=A007089(n)
    return int(x[-1]+x[:-1], 3) # Indranil Ghosh, Feb 03 2017