A054043 -id:A054043 - cp's OEIS frontend

A054016 a(n) = smallest nonnegative integer not the Nim sum of at most 4 earlier terms.

1, 2, 4, 8, 16, 31, 32, 64, 103, 128, 171, 213, 256, 301, 342, 439, 475, 494, 512, 558, 595, 911, 1024, 1075, 1114, 1189, 1287, 1606, 1727, 1996, 2048, 2102, 2140, 2225, 2339, 2667, 2691, 3240, 3733, 4096, 4153, 4171, 4371, 4745, 4912, 5237, 5601, 5746

Offset: 1

N. J. A. Sloane, Apr 29 2000

Grundy function for turn-at-most-5-coins game.

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see Table 3, Chapter 14, p. 433.

A. S. Fraenkel, Mathematical Chats Between Two Physicists, in Puzzlers' Tribute: A Feast for the Mind, honoring Martin Gardner (D. Wolfe and T. Rodgers, eds.), A. K. Peters, 2002, pp. 315-325.
Index entries for sequences related to Nim-sums

Cf. A000069, A033623, A054043, etc.

More terms from Larry Reeves (larryr(AT)acm.org), Oct 31 2000

A033623 Grundy function for turn-at-most-4-coins game.

Original entry on oeis.org

1, 2, 4, 8, 15, 16, 32, 51, 64, 85, 106, 128, 150, 171, 219, 237, 247, 256, 279, 297, 455, 512, 537, 557, 594, 643, 803, 863, 998, 1024, 1051, 1070, 1112, 1169, 1333, 1345, 1620, 1866, 2048, 2076, 2085, 2185, 2372

Offset: 1

David A. Madore

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Table 3, page 433.

Cf. A000069, A054016, A054043, etc.

Clear[a]; a[1] = 1; a[n_] := a[n] = (xor = BitXor @@@ Subsets[Array[a, n-1], 3] // Union ; r = Range[0, m = Last[xor]]; cp = Complement[r, xor]; If[cp == {}, m+1, First[cp]]); Table[a[n], {n, 1, 43}] (* Jean-François Alcover, Jan 09 2013 *)

a(n)=smallest natural not the exclusive-or of at most three a(k) for k

More terms from N. J. A. Sloane Apr 29 2000

A054041 Sum of a(n) terms of 1/k^(1/3) first exceeds n.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 10, 12, 15, 17, 20, 23, 25, 28, 32, 35, 38, 41, 45, 49, 52, 56, 60, 64, 68, 72, 76, 81, 85, 89, 94, 98, 103, 108, 113, 117, 122, 127, 132, 138, 143, 148, 153, 159, 164, 170, 175, 181, 187, 192, 198, 204, 210, 216, 222, 228, 234, 240, 247, 253, 259

Offset: 0

Asher Auel, Apr 13 2000

nonn

Cf. A002387, A054043, A019529.

s = 0; k = 1; Do[ While[ s <= n, s = s + N[ 1/k^(1/3), 24 ]; k++ ]; Print[ k - 1 ], {n, 1, 75} ]

Corrected and extended by Robert G. Wilson v, Aug 01 2000

Edited by N. J. A. Sloane, Jan 17 2009 at the suggestion of R. J. Mathar

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A054016 a(n) = smallest nonnegative integer not the Nim sum of at most 4 earlier terms.

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A033623 Grundy function for turn-at-most-4-coins game.

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A054041 Sum of a(n) terms of 1/k^(1/3) first exceeds n.

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