A001965 - OEIS

%I M2301 N0907 #41 Aug 26 2022 02:49:29

%S 0,1,3,4,5,6,8,9,10,11,12,14,15,16,17,19,20,21,22,24,25,26,27,29,30,

%T 31,32,33,35,36,37,38,40,41,42,43,45,46,47,48,50,51,52,53,55,56,57,58,

%U 59,61,62,63,64,66,67,68,69,71,72,73,74,76,77,78,79,80,82

%N u-pile count for the 4-Wythoff game with i=2.

%C See Connell (1959) for further information.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001965/b001965.txt">Table of n, a(n) for n = 0..10000</a>

%H Ian G. Connell, <a href="http://dx.doi.org/10.4153/CMB-1959-024-3">A generalization of Wythoff's game</a>, Canad. Math. Bull. 2 (1959) 181-190.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HofstadterG-Sequence.html">Hofstadter G-Sequence</a>

%F a(n) = floor( (n+1/2)*(sqrt(5)-1) ). - _R. J. Mathar_, Feb 14 2011

%F a(n) = A005206(2*n). - _Peter Bala_, Aug 09 2022

%F a(n) = A001966(n)-4*n-2. - _Chai Wah Wu_, Aug 25 2022

%t Table[Floor[(n + 1/2)*(Sqrt[5] - 1)], {n, 0, 100}] (* _T. D. Noe_, Aug 17 2012 *)

%o (Python)

%o from math import isqrt

%o def A001965(n): return ((m:=(n<<1)+1)+isqrt(5*m**2)>>1)-m # _Chai Wah Wu_, Aug 25 2022

%Y Complement of A001966 (the v-pile). Cf. A001961, A005206.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_

%E Edited by _Hugo Pfoertner_, Dec 27 2021