A255590 - OEIS

%I #31 Feb 03 2017 04:43:03

%S 0,1,2,3,4,1,6,11,16,21,2,7,12,17,22,3,8,13,18,23,4,9,14,19,24,5,30,

%T 55,80,105,6,31,56,81,106,7,32,57,82,107,8,33,58,83,108,9,34,59,84,

%U 109,10,35,60,85,110,11,36,61,86,111,12,37,62,87,112,13,38,63,88

%N Convert n to base 5, move the least significant digit to the most significant one and convert back to base 10.

%C a(5*n) = n.

%C a(5^n) = 5^(n-1).

%C Fixed points of the transform are listed in A048330.

%H Indranil Ghosh, <a href="/A255590/b255590.txt">Table of n, a(n) for n = 0..15625</a> (terms 0..1000 from Paolo P. Lava)

%e 14 in base 5 is 24: moving the least significant digit to the most significant one we have 42 that is 22 in base 10.

%p with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);

%p for n from 1 to q do

%p 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]];

%p a:=convert(a,base,h,10); b:=0; for k from nops(a) by -1 to 1 do b:=10*b+a[k]; od;

%p print(b); od; end: P(10^4,5);

%t roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 5; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 68]) (* _Michael De Vlieger_, Mar 04 2015 *)

%o (Python)

%o def A255590(n):

%o ....x=str(A007091(n))

%o ....return int(x[-1]+x[:-1], 5) # _Indranil Ghosh_, Feb 03 2017

%Y Cf. A030104, A038572, A048330, A255588, A255589, A255591-A255594, A048787, A255689-A255693.

%K nonn,easy,base

%O 0,3

%A _Paolo P. Lava_, Mar 02 2015