A255689 Convert n to base 4, move the most significant digit to the least significant one and convert back to base 10.

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

Offset: 0

Author

Paolo P. Lava, Mar 02 2015

Keywords

• nonn
• easy
• base

Comments

a(4*n) = 1.

Fixed points of the transform are listed in A048329.

Examples

			11 in base 4 is 23: moving the most significant digit as the least significant one we have 32 that is 14 in base 10.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..65536 (terms 0..1000 from Paolo P. Lava)

Crossrefs

Cf. A006257, A030103, A255588-A255594, A048787, A255690-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 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(10^4,4);

Mathematica

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 4; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 70]) (* Michael De Vlieger, Mar 04 2015 *)
Table[FromDigits[RotateLeft[IntegerDigits[n,4]],4],{n,0,70}] (* Harvey P. Dale, Aug 07 2015 *)

Python

def A255689(n):
    x=A007090(n)
    return int (x[1:]+x[0],4) # Indranil Ghosh, Feb 08 2017