A255693 Convert n to base 8, move the most significant digit to the least significant one and convert back to base 10.

0, 1, 2, 3, 4, 5, 6, 7, 1, 9, 17, 25, 33, 41, 49, 57, 2, 10, 18, 26, 34, 42, 50, 58, 3, 11, 19, 27, 35, 43, 51, 59, 4, 12, 20, 28, 36, 44, 52, 60, 5, 13, 21, 29, 37, 45, 53, 61, 6, 14, 22, 30, 38, 46, 54, 62, 7, 15, 23, 31, 39, 47, 55, 63, 1, 9, 17, 25, 33, 41

Offset: 0

Author

Paolo P. Lava, Mar 02 2015

Keywords

• nonn
• easy
• base

Comments

a(8*n) = 1.

Fixed points of the transform are listed in A048333.

Examples

			13 in base 8 is 15: moving the most significant digit as the least significant one we have 51 that is 41 in base 10.
		

Links

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

Crossrefs

Cf. A006257, A030107, A255588-A255594, A255689-A255692.

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 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(10^4,8);

Mathematica

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 8; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* Michael De Vlieger, Mar 04 2015 *)