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A255693 Convert n to base 8, move the most significant digit to the least significant one and convert back to base 10.

%I A255693 #20 Mar 14 2015 14:20:47
%S A255693 0,1,2,3,4,5,6,7,1,9,17,25,33,41,49,57,2,10,18,26,34,42,50,58,3,11,19,
%T A255693 27,35,43,51,59,4,12,20,28,36,44,52,60,5,13,21,29,37,45,53,61,6,14,22,
%U A255693 30,38,46,54,62,7,15,23,31,39,47,55,63,1,9,17,25,33,41
%N A255693 Convert n to base 8, move the most significant digit to the least significant one and convert back to base 10.
%C A255693 a(8*n) = 1.
%C A255693 Fixed points of the transform are listed in A048333.
%H A255693 Paolo P. Lava, <a href="/A255693/b255693.txt">Table of n, a(n) for n = 0..1000</a>
%e A255693 13 in base 8 is 15: moving the most significant digit as the least significant one we have 51 that is 41 in base 10.
%p A255693 with(numtheory): P:=proc(q,h) local a,b,k,n; print(0);
%p A255693 for n from 1 to q do
%p A255693 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 A255693 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 A255693 print(b); od; end: P(10^4,8);
%t A255693 roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Append[Rest@ w, First@ w]]; b = 8; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 69]) (* _Michael De Vlieger_, Mar 04 2015 *)
%Y A255693 Cf. A006257, A030107, A255588-A255594, A255689-A255692.
%K A255693 nonn,easy,base
%O A255693 0,3
%A A255693 _Paolo P. Lava_, Mar 02 2015