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

0,3

Comments

a(3*n) = n.

Fixed points of the transform are listed in A048328.

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A030102, A038572, A048328, A255589-A255594, A048787, A255689-A255693.

Sequence in context: A048787 A030102 A072010 * A328034 A123360 A072015

Adjacent sequences: A255585 A255586 A255587 * A255589 A255590 A255591

Keyword

nonn,easy,base

Author

Paolo P. Lava, Feb 27 2015

Status

approved