A255692 Convert n to base 7, move the most significant digit to the least significant one and convert back to base 10.

0, 1, 2, 3, 4, 5, 6, 1, 8, 15, 22, 29, 36, 43, 2, 9, 16, 23, 30, 37, 44, 3, 10, 17, 24, 31, 38, 45, 4, 11, 18, 25, 32, 39, 46, 5, 12, 19, 26, 33, 40, 47, 6, 13, 20, 27, 34, 41, 48, 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99, 106, 113, 120, 127, 134

Offset

0,3

Comments

a(7*n) = 1.

Fixed points of the transform are listed in A048332.

Links

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

Example

11 in base 7 is 14: moving the most significant digit as the least significant one we have 41 that is 29 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, 7);

Mathematica

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 7; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 68]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateLeft[IntegerDigits[n, 7]], 7], {n, 0, 70}] (* Harvey P. Dale, Oct 20 2020 *)

Crossrefs

Cf. A006257, A030106, A255588-A255594, A255689-A255691, A255693.

Sequence in context: A328018 A242603 A106608 * A030106 A255592 A037894

Adjacent sequences: A255689 A255690 A255691 * A255693 A255694 A255695

Keyword

nonn,easy,base

Author

Paolo P. Lava, Mar 02 2015

Status

approved