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

Author

Paolo P. Lava, Mar 02 2015

Keywords

• nonn
• easy
• base

Comments

a(6*n) = n.

Fixed points of the transform are listed in A048331.

Examples

			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.
		

Links

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

Crossrefs

Cf. A030105, A038572, A048331, A255588-A255590, A255592-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(10^4,6);

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 *)

Python

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