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

%I A255589 #38 May 19 2025 23:45:31
%S A255589 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,
%T A255589 54,7,23,39,55,8,24,40,56,9,25,41,57,10,26,42,58,11,27,43,59,12,28,44,
%U A255589 60,13,29,45,61,14,30,46,62,15,31,47,63,16,80,144,208,17,81
%N A255589 Convert n to base 4, move the least significant digit to the most significant one and convert back to base 10.
%C A255589 Fixed points of the transform are listed in A048329.
%H A255589 Indranil Ghosh, <a href="/A255589/b255589.txt">Table of n, a(n) for n = 0..16384</a> (terms 0..1000 from Paolo P. Lava)
%F A255589 a(4*k) = k.
%F A255589 a(4^k) = 4^(k-1).
%e A255589 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.
%p A255589 with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
%p A255589 for n from 1 to q do
%p A255589 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 A255589 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 A255589 print(b); od; end: P(10^4,4);
%t A255589 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 *)
%t A255589 Array[FromDigits[RotateRight[IntegerDigits[#,4]],4]&,70,0] (* _Harvey P. Dale_, Mar 01 2016 *)
%o A255589 (Python)
%o A255589 def A255589(n):
%o A255589     x=str(A007090(n))
%o A255589     return int(x[-1]+x[:-1],4) # _Indranil Ghosh_, Feb 03 2017
%Y A255589 Cf. A030103, A038572, A048329, A255588, A255590-A255594, A048787, A255689-A255693.
%K A255589 nonn,easy,base
%O A255589 0,3
%A A255589 _Paolo P. Lava_, Mar 02 2015