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

Author

Dylan Hamilton, Jul 02 2015

Keywords

• nonn
• base
• easy

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).

Crossrefs

Cf. A030101, A055945.

Programs

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

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 *)

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

Extensions

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