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A001965 u-pile count for the 4-Wythoff game with i=2.
(Formerly M2301 N0907)
4
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, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
See Connell (1959) for further information.
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190.
Eric Weisstein's World of Mathematics, Hofstadter G-Sequence
FORMULA
a(n) = floor( (n+1/2)*(sqrt(5)-1) ). - R. J. Mathar, Feb 14 2011
a(n) = A005206(2*n). - Peter Bala, Aug 09 2022
a(n) = A001966(n)-4*n-2. - Chai Wah Wu, Aug 25 2022
MATHEMATICA
Table[Floor[(n + 1/2)*(Sqrt[5] - 1)], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)
PROG
(Python)
from math import isqrt
def A001965(n): return ((m:=(n<<1)+1)+isqrt(5*m**2)>>1)-m # Chai Wah Wu, Aug 25 2022
CROSSREFS
Complement of A001966 (the v-pile). Cf. A001961, A005206.
Sequence in context: A025020 A028974 A184427 * A039178 A110911 A103202
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by Hugo Pfoertner, Dec 27 2021
STATUS
approved

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Last modified April 22 06:39 EDT 2024. Contains 371888 sequences. (Running on oeis4.)