A283770 - OEIS

%I #13 Dec 06 2019 16:24:08

%S 1,3,10,12,14,16,23,25,27,29,34,36,38,40,42,47,49,51,53,55,60,62,64,

%T 66,73,75,77,79,86,88,90,92,99,101,103,105,112,114,116,118,123,125,

%U 127,129,131,136,138,140,142,144,149,151,153,155,162,164,166,168,175

%N Numbers k such that L(k) = 1 mod 3, where L = A000201 = lower Wythoff sequence.

%C The sequences A283769, A283770, A283771 partition the positive integers.

%H Clark Kimberling, <a href="/A283770/b283770.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n+1) - a(n) is in {2,5,7} for every n.

%t r = GoldenRatio; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];

%t Flatten[Position[u, 0]]  (* A283769 *)

%t Flatten[Position[u, 1]]  (* A283770 *)

%t Flatten[Position[u, 2]]  (* A283771 *)

%o (PARI)

%o r = (1 + sqrt(5))/2;

%o for(n=1, 351, if(floor(n*r)%3==1, print1(n, ", "))) \\ _Indranil Ghosh_, Mar 19 2017

%o (Python)

%o import math

%o from sympy import sqrt

%o r = (1 + sqrt(5))/2

%o [n for n in range(1, 351) if int(math.floor(n*r))%3==1] # _Indranil Ghosh_, Mar 19 2017

%Y Cf. A000201, A001622, A283769, A283771.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Mar 18 2017