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.

User: George Pollard

George Pollard's wiki page.

George Pollard has authored 4 sequences.

A183192 Length of shortest winning opening sequences for Dakon-n.

Original entry on oeis.org

12, 24, 19, 25, 29
Offset: 4

Views

Author

George Pollard, Dec 15 2011

Keywords

Comments

Dakon-n is the game of Dakon, with n small holes per player. This sequence records the minimum number of moves in a play which wins outright on the starting player's first turn. The best-known values for 9 and 10 holes are 41 and 68, respectively.

References

  • J. Donkers, A. de Voogt and J. Uiterwijk, Human versus Machine Problem-Solving: Winning Openings in Dakon, Board Game Studies 3 (2000), 79-88.

Extensions

Corrected the offset.

A183193 Minimum number of counters left after a winning opening move for Dakon-n.

Original entry on oeis.org

2, 4, 2, 2, 3, 3, 4
Offset: 4

Views

Author

George Pollard, Dec 15 2011

Keywords

Comments

Dakon-n is the game of Dakon played with n small holes per player. This sequence records the minimum number of counters left for a particular n, after the starting player wins on their first turn.

References

  • J. Donkers, A. de Voogt and J. Uiterwijk, Human versus Machine Problem-Solving: Winning Openings in Dakon, Board Game Studies 3 (2000), 79-88.

A202258 Minimum number of laps for a starting player's win in Dakon-n.

Original entry on oeis.org

8, 6, 5, 5, 4
Offset: 4

Views

Author

George Pollard, Dec 15 2011

Keywords

Comments

Dakon-n is the game of Dakon with n small holes per player. This sequence records the minimum number of times a starting player can lap the board, while winning on the first turn. The best-known value for n=9,10 is 5.

References

  • J. Donkers, A. de Voogt and J. Uiterwijk, Human versus Machine Problem-Solving: Winning Openings in Dakon, Board Game Studies 3 (2000), 79-88.

A137331 a(n) = 1 if the binary weight of n is prime, otherwise 0.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1
Offset: 0

Views

Author

George Pollard, Apr 07 2008

Keywords

Examples

			a(0) = 0 (binary). Bits set = 0, 0 not prime -> 0.
a(1) = 1 (binary). Bits set = 1, 1 not prime -> 0.
a(2) = 10 (binary). Bits set = 1, 1 not prime -> 0.
a(3) = 11 (binary). Bits set = 2, 2 prime -> 1.

Crossrefs

Begins the same as A135136, but differs starting at a(31).

Programs

  • Maple
    A000120 := proc(n) add(i,i=convert(n,base,2)) ; end: A010051 := proc(n) if isprime(n) then 1 ; else 0 ; fi ; end: A137331 := proc(n) A010051(A000120(n)) ; end: seq(A137331(n),n=0..200) ; # R. J. Mathar, Apr 09 2008
  • Mathematica
    Table[If[PrimeQ[Plus @@ IntegerDigits[n, 2]], 1, 0], {n, 0, 100}] (* Stefan Steinerberger, Apr 09 2008 *)
  • PARI
    f(n)={v=binary(n);s=0;for(k=1,#v,if(v[k]== 1,s++));return(isprime(s))};for(n=0,104,if(f(n),print1("1, "),print1("0, "))) \\ Washington Bomfim, Jan 14 2011

Formula

a(n) = A010051(A000120(n)). - R. J. Mathar, Apr 09 2008

Extensions

More terms from R. J. Mathar and Stefan Steinerberger, Apr 09 2008

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

Content is available under The OEIS End-User License Agreement.