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A255588
Convert n to base 3, move the least significant digit to the most significant one and convert back to base 10.
13
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
KEYWORD
nonn,easy,base
AUTHOR
Paolo P. Lava, Feb 27 2015
STATUS
approved