A188012 Positions of 0 in A188011; complement of A188013.

3, 8, 16, 21, 29, 37, 42, 50, 55, 63, 71, 76, 84, 92, 97, 105, 110, 118, 126, 131, 139, 144, 152, 160, 165, 173, 181, 186, 194, 199, 207, 215, 220, 228, 236, 241, 249, 254, 262, 270, 275, 283, 288, 296, 304, 309, 317, 325, 330, 338, 343, 351, 359, 364, 372, 377, 385, 393, 398, 406, 414, 419, 427, 432, 440

Offset: 1

Author

Clark Kimberling, Mar 19 2011

Keywords

• nonn

Comments

See A188014 and A188011.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A188011, A188013, A188014.

Programs

Magma

[3*Floor((n-1)*(1+Sqrt(5))/2)+2*n+1: n in [1..65]]; // G. C. Greubel, Nov 22 2018

Mathematica

r=(1+5^(1/2))/2; k=3;
t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r],{n,1,220}]   (* A188011 *)
Flatten[Position[t,0]]  (* A188012 *)
Flatten[Position[t,1]]  (* A188013 *)
Table[3*Floor[(n-1)*GoldenRatio] + 2*n + 1, {n, 1, 65}] (* G. C. Greubel, Nov 22 2018 *)

PARI

vector(65, n, 3*floor((n-1)*(1+sqrt(5))/2)+2*n+1) \\ G. C. Greubel, Nov 22 2018

Sage

[3*floor((n-1)*(1+sqrt(5))/2)+2*n+1 for n in (1..65)] # G. C. Greubel, Nov 22 2018

Formula

a(n+1) = 3*floor(n*phi)+2*n+3 for n>=0, where phi = (1+sqrt(5))/2 (see A188011). - Michel Dekking, Sep 28 2017