A259658 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.

0, 1, 2, 11, 38, 271, 544, 2093, 2624, 8607, 17984, 35343, 35904, 70671, 71744, 141327, 143424, 282639, 286784, 565263, 573504, 1130511, 1146944, 2261007, 2293824, 4521999, 4587584, 9043983, 9175104, 18087951, 18350144, 36175887, 36700224, 72351759, 73400384

Offset

0,3

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2).

Formula

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

Mathematica

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 *)
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 *)

Prog

(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

Crossrefs

Cf. A030101, A055945.

Sequence in context: A166989 A143550 A259213 * A350952 A000175 A276659

Adjacent sequences: A259655 A259656 A259657 * A259659 A259660 A259661

Keyword

nonn,base,easy

Author

Dylan Hamilton, Jul 02 2015

Extensions

a(0), a(19)-a(34) from Alois P. Heinz, Jul 02 2015

Status

approved