A255592 - OEIS

%I #28 Jan 27 2023 11:26:50

%S 0,1,2,3,4,5,6,1,8,15,22,29,36,43,2,9,16,23,30,37,44,3,10,17,24,31,38,

%T 45,4,11,18,25,32,39,46,5,12,19,26,33,40,47,6,13,20,27,34,41,48,7,56,

%U 105,154,203,252,301,8,57,106,155,204,253,302,9,58,107,156

%N Convert n to base 7, move least significant digit to most significant digit and convert back to base 10.

%C a(7*n) = n.

%C a(7^n) = 7^(n-1).

%C Fixed points of the transform are listed in A048332.

%H Paolo P. Lava, <a href="/A255592/b255592.txt">Table of n, a(n) for n = 0..1000</a>

%e 11 in base 7 is 14: moving the least significant digit to the most significant one we have 41 that is 29 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(10^4,7);

%t roll[n_, b_] := Block[{w = IntegerDigits[n, b]}, Prepend[Most@ w, Last@ w]]; b = 7; FromDigits[#, b] & /@ (roll[#, b] & /@ Range[0, 66]) (* _Michael De Vlieger_, Mar 04 2015 *)

%t Table[FromDigits[RotateRight[IntegerDigits[n,7]],7],{n,0,100}] (* _Harvey P. Dale_, Jan 27 2023 *)

%Y Cf. A030106, A038572, A048332, A255588-A255591, A255593, A255594, A048787, A255689-A255693.

%K nonn,easy,base

%O 0,3

%A _Paolo P. Lava_, Mar 02 2015