A255691 Convert n to base 6, move the most significant digit to the least significant one 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, 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175

Offset

0,3

Comments

a(6*n) = 1.

Fixed points of the transform are listed in A048331.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Example

16 in base 6 is 24: moving the most significant digit as the least 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 1 to nops(a)-1 do b:=[op(b), a[k]]; od; a:=[a[nops(a)], op(b)];
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]}, Append[Rest@ w, First@ w]]; b = 6; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 65]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateLeft[IntegerDigits[n, 6]], 6], {n, 0, 70}] (* Harvey P. Dale, Mar 02 2023 *)

Crossrefs

Cf. A006257, A030105, A255588-A255594, A255689-A255690, A255692-A255693.

Sequence in context: A319654 A244414 A214394 * A030105 A255591 A324395

Adjacent sequences: A255688 A255689 A255690 * A255692 A255693 A255694

Keyword

nonn,easy,base

Author

Paolo P. Lava, Mar 02 2015

Status

approved