A255589 Convert n to base 4, move the least significant digit to the most significant one and convert back to base 10.

0, 1, 2, 3, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 4, 20, 36, 52, 5, 21, 37, 53, 6, 22, 38, 54, 7, 23, 39, 55, 8, 24, 40, 56, 9, 25, 41, 57, 10, 26, 42, 58, 11, 27, 43, 59, 12, 28, 44, 60, 13, 29, 45, 61, 14, 30, 46, 62, 15, 31, 47, 63, 16, 80, 144, 208, 17, 81

Offset: 0

Author

Paolo P. Lava, Mar 02 2015

Keywords

• nonn
• easy
• base

Comments

Fixed points of the transform are listed in A048329.

Examples

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

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..16384 (terms 0..1000 from Paolo P. Lava)

Crossrefs

Cf. A030103, A038572, A048329, A255588, A255590-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(10^4,4);

Mathematica

roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 4; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* Michael De Vlieger, Mar 04 2015 *)
Array[FromDigits[RotateRight[IntegerDigits[#,4]],4]&,70,0] (* Harvey P. Dale, Mar 01 2016 *)

Python

def A255589(n):
    x=str(A007090(n))
    return int(x[-1]+x[:-1],4) # Indranil Ghosh, Feb 03 2017

Formula

a(4*k) = k.

a(4^k) = 4^(k-1).