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A255590 Convert n to base 5, move the least significant digit to the most significant one and convert back to base 10.

%I A255590 #35 Jun 11 2025 16:40:39
%S A255590 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 A255590 55,80,105,6,31,56,81,106,7,32,57,82,107,8,33,58,83,108,9,34,59,84,
%U A255590 109,10,35,60,85,110,11,36,61,86,111,12,37,62,87,112,13,38,63,88
%N A255590 Convert n to base 5, move the least significant digit to the most significant one and convert back to base 10.
%C A255590 a(5*n) = n.
%C A255590 a(5^n) = 5^(n-1).
%C A255590 Fixed points of the transform are listed in A048330.
%H A255590 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 A255590 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 A255590 with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
%p A255590 for n from 1 to q do
%p A255590 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 A255590 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 A255590 print(b); od; end: P(10^4,5);
%t A255590 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 *)
%t A255590 Table[FromDigits[RotateRight[IntegerDigits[n,5]],5],{n,0,100}] (* _Harvey P. Dale_, Jun 11 2025 *)
%o A255590 (Python)
%o A255590 def A255590(n):
%o A255590     x=str(A007091(n))
%o A255590     return int(x[-1]+x[:-1], 5) # _Indranil Ghosh_, Feb 03 2017
%Y A255590 Cf. A030104, A038572, A048330, A255588, A255589, A255591-A255594, A048787, A255689-A255693.
%K A255590 nonn,easy,base
%O A255590 0,3
%A A255590 _Paolo P. Lava_, Mar 02 2015