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A255689 Convert n to base 4, move the most significant digit to the least significant one and convert back to base 10.

%I A255689 #28 May 22 2025 10:21:42
%S A255689 0,1,2,3,1,5,9,13,2,6,10,14,3,7,11,15,1,5,9,13,17,21,25,29,33,37,41,
%T A255689 45,49,53,57,61,2,6,10,14,18,22,26,30,34,38,42,46,50,54,58,62,3,7,11,
%U A255689 15,19,23,27,31,35,39,43,47,51,55,59,63,1,5,9,13,17,21,25
%N A255689 Convert n to base 4, move the most significant digit to the least significant one and convert back to base 10.
%C A255689 a(4*n) = 1.
%C A255689 Fixed points of the transform are listed in A048329.
%H A255689 Indranil Ghosh, <a href="/A255689/b255689.txt">Table of n, a(n) for n = 0..65536</a> (terms 0..1000 from Paolo P. Lava)
%e A255689 11 in base 4 is 23: moving the most significant digit as the least significant one we have 32 that is 14 in base 10.
%p A255689 with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
%p A255689 for n from 1 to q do
%p A255689 a:=convert(n,base,h); b:=[]; for k from 1 to nops(a)-1 do b:=[op(b),a[k]]; od; a:=[a[nops(a)],op(b)];
%p A255689 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 A255689 print(b); od; end: P(10^4,4);
%t A255689 roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 4; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 70]) (* _Michael De Vlieger_, Mar 04 2015 *)
%t A255689 Table[FromDigits[RotateLeft[IntegerDigits[n,4]],4],{n,0,70}] (* _Harvey P. Dale_, Aug 07 2015 *)
%o A255689 (Python)
%o A255689 def A255689(n):
%o A255689     x=A007090(n)
%o A255689     return int (x[1:]+x[0],4) # _Indranil Ghosh_, Feb 08 2017
%Y A255689 Cf. A006257, A030103, A255588-A255594, A048787, A255690-A255693.
%K A255689 nonn,easy,base
%O A255689 0,3
%A A255689 _Paolo P. Lava_, Mar 02 2015