A255592 Convert n to base 7, move least significant digit to most significant digit 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, 7, 56, 105, 154, 203, 252, 301, 8, 57, 106, 155, 204, 253, 302, 9, 58, 107, 156

Offset: 0

Author

Paolo P. Lava, Mar 02 2015

Keywords

• nonn
• easy
• base

Comments

a(7*n) = n.

a(7^n) = 7^(n-1).

Fixed points of the transform are listed in A048332.

Examples

			11 in base 7 is 14: moving the least significant digit to the most significant one we have 41 that is 29 in base 10.
		

Links

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

Crossrefs

Cf. A030106, A038572, A048332, A255588-A255591, A255593, 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(10^4,7);

Mathematica

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 7; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 66]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateRight[IntegerDigits[n,7]],7],{n,0,100}] (* Harvey P. Dale, Jan 27 2023 *)