cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A006019 Remoteness number of n in Simon Norton's game of Tribulations.

Original entry on oeis.org

0, 1, 2, 1, 6, 3, 1, 5, 3, 2, 1, 2, 3, 4, 3, 1, 9, 3, 6, 7, 8, 1, 10, 3, 2, 3, 4, 5, 1, 4, 3, 8, 7, 5, 9, 7, 1, 14, 3, 4, 7, 4, 2, 9, 4, 1, 2, 3, 4, 7, 8, 12, 16, 9, 3, 1, 12, 3, 14, 7, 6, 4, 8, 6, 3, 2, 1, 6, 3, 5, 7, 11, 4
Offset: 0

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Author

N. J. A. Sloane

Keywords

Comments

The game of Tribulations is similar to Epstein's game in A005240, but the number of chips to be put or taken is the largest triangular number not larger than C: C-> C +- A057944(C). The remoteness is the number of moves in the game if the initial heap has n chips and both players play the optimum strategy. - R. J. Mathar, May 06 2016

Examples

			For all positive triangular numbers (A000217) the remoteness is 1, because the starting player uses the strategy to take all of the chips and the game is over. The remoteness of 2 is 2, because taking one or putting one in the first move leads anyway to a n with remoteness 1. The remoteness of 4 is 6: 4 -> 7 -> 13 -> 23 -> 2 -> (1 or 3) -> 0. - _R. J. Mathar_, May 06 2016

References

  • E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 502.
  • R. K. Guy, Fair Game: How to play impartial combinatorial games, COMAP's Mathematical Exploration Series, 1989; see p. 88.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

See A266726 for indices of even-valued terms (losing positions).

Extensions

Name and offset corrected by N. J. A. Sloane, Jan 03 2016

A005241 N-positions in Epstein's Put or Take a Square game.

Original entry on oeis.org

1, 4, 9, 11, 14, 16, 21, 25, 30, 36, 41, 44, 49, 52, 54, 64, 69, 71, 81, 84, 86, 92, 100, 105, 120, 121, 126, 136, 141, 144, 149, 164, 169, 174, 189, 196, 201, 208, 216, 225, 230, 245, 252
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, E26.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A005240.

A259963 Exceptional N-positions for Epstein's Put or Take a Square game.

Original entry on oeis.org

11, 44, 52, 71, 84, 92, 136, 208, 252, 284, 291, 296, 436, 444, 468, 491, 601, 704, 832, 918, 933, 976, 1164, 1169, 1184, 1276, 1291, 1558, 1684, 1699, 1708, 1724, 1837, 1856, 2028, 2080, 2123, 2389, 2412, 2536, 2619, 2624, 2664
Offset: 1

Views

Author

N. J. A. Sloane, Jul 10 2015

Keywords

References

  • R. K. Guy, Letter to N. J. A. Sloane, Aug 01, 1975.

Links

Crossrefs

A subset of A005241. Cf. A005242.

A340780 Losing positions n (P-positions) in the following game: two players take turns dividing the current value of n by either a prime power > 1 or by A007947(n) to obtain the new value of n. The winner is the player whose division results in 1.

Original entry on oeis.org

1, 12, 18, 20, 28, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 120, 124, 147, 148, 153, 164, 168, 171, 172, 175, 188, 207, 212, 216, 236, 242, 244, 245, 261, 264, 268, 270, 275, 279, 280, 284, 292, 312, 316, 325, 332, 333, 338, 356, 363, 369, 378, 387, 388
Offset: 1

Views

Author

José María Grau Ribas, Jan 21 2021

Keywords

Comments

The game is equivalent to the game of Nim with the additional allowed move consisting of removing one object from each pile.

Crossrefs

Cf. A003557, A227691, A227763, A227764, A171947, A005240, A081691, A099352, A171945, A171949, A285304, A120442, A137295, A275432.

Programs

  • Mathematica
    Clear[moves,los]; A003557[n_]:= {Module[{aux = FactorInteger[n], L=Length[FactorInteger[n]]},Product[aux[[i,1]]^(aux[[i, 2]]-1),{i, L}]]};
moves[n_] :=moves[n] = Module[{aux = FactorInteger[n], L=Length[ FactorInteger [n]]}, Union[Flatten[Table[n/aux[[i,1]]^j, {i,1,L},{j,1,aux[[i,2]]}],1], A003557[n]]]; los[1]=True; los[m_] := los[m] = If[PrimeQ[m], False, Union@Flatten@Table[los[moves[m][[i]]], {i,1,Length[moves[m]]}] == {False}]; Select[Range[400], los]
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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