A255591 Convert n to base 6, move least significant digit to most significant digit and convert back to base 10.

0, 1, 2, 3, 4, 5, 1, 7, 13, 19, 25, 31, 2, 8, 14, 20, 26, 32, 3, 9, 15, 21, 27, 33, 4, 10, 16, 22, 28, 34, 5, 11, 17, 23, 29, 35, 6, 42, 78, 114, 150, 186, 7, 43, 79, 115, 151, 187, 8, 44, 80, 116, 152, 188, 9, 45, 81, 117, 153, 189, 10, 46, 82, 118, 154, 190, 11

Offset

0,3

Comments

a(6*n) = n.

Fixed points of the transform are listed in A048331.

Links

Indranil Ghosh, Table of n, a(n) for n = 0..46656 (terms 0..1000 from Paolo P. Lava)

Example

16 in base 6 is 24: moving the least significant digit to the most significant one we have 42 that is 26 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, 6);

Mathematica

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 6; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 66]) (* Michael De Vlieger, Mar 04 2015 *)

Prog

(Python)
def A255591(n):
....x=A007092(n)
....return int(x[-1]+x[:-1], 6) # Indranil Ghosh, Feb 03 2017

Crossrefs

Cf. A030105, A038572, A048331, A255588-A255590, A255592-A255594, A048787, A255689-A255693.

Sequence in context: A214394 A255691 A030105 * A324395 A350112 A037893

Adjacent sequences: A255588 A255589 A255590 * A255592 A255593 A255594

Keyword

nonn,easy,base

Author

Paolo P. Lava, Mar 02 2015

Status

approved