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

0,3

Comments

Fixed points of the transform are listed in A048329.

Links

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

Formula

a(4*k) = k.

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A030103, A038572, A048329, A255588, A255590-A255594, A048787, A255689-A255693.

Sequence in context: A080409 A255689 A030103 * A290053 A105640 A090299

Adjacent sequences: A255586 A255587 A255588 * A255590 A255591 A255592

Keyword

nonn,easy,base

Author

Paolo P. Lava, Mar 02 2015

Status

approved