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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 T. D. Noe, Table of n, a(n) for n = 0..10000 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 Adjacent sequences: A001962 A001963 A001964 * A001966 A001967 A001968 KEYWORD nonn,easy AUTHOR N. J. A. Sloane 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.)