A259658 - OEIS

%I #22 Nov 23 2022 13:27:28

%S 0,1,2,11,38,271,544,2093,2624,8607,17984,35343,35904,70671,71744,

%T 141327,143424,282639,286784,565263,573504,1130511,1146944,2261007,

%U 2293824,4521999,4587584,9043983,9175104,18087951,18350144,36175887,36700224,72351759,73400384

%N Let f(x) be the absolute value of the difference between x and its base-2 reversal. Let g(x) be the number of times f(x) must be applied to x for the result to be 0. a(n) is the smallest value of x for which g(x) is n.

%C f(x) = abs(A055945(x)).

%H Alois P. Heinz, <a href="/A259658/b259658.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-2).

%F G.f.: -x*(18144*x^12 +12800*x^11 -13708*x^10 -11200*x^9 -2870*x^8 -1068*x^7 -1302*x^6 -434*x^5 -240*x^4 -32*x^3 -8*x^2 -2*x-1)/ ((x-1) *(x+1) *(2*x^2-1)). - _Alois P. Heinz_, Jul 02 2015

%t CoefficientList[Series[x (18144 x^12 + 12800 x^11 - 13708 x^10 -11200 x^9 - 2870 x^8 - 1068 x^7 - 1302 x^6 - 434 x^5 - 240 x^4 - 32 x^3 - 8 x^2 - 2 x - 1)/((1 - x) (x + 1) (2 x^2 - 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jul 10 2015 *)

%t LinearRecurrence[{0,3,0,-2},{0,1,2,11,38,271,544,2093,2624,8607,17984,35343,35904,70671},50] (* _Harvey P. Dale_, Nov 23 2022 *)

%o (Magma) I:=[0,1,2,11,38,271,544,2093,2624, 8607,17984,35343, 35904,70671]; [n le 14 select I[n] else 3*Self(n-2)-2*Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jul 10 2015

%Y Cf. A030101, A055945.

%K nonn,base,easy

%O 0,3

%A _Dylan Hamilton_, Jul 02 2015

%E a(0), a(19)-a(34) from _Alois P. Heinz_, Jul 02 2015