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 1-7 of 7 results.

A054517 Duplicate of A054016.

Original entry on oeis.org

1, 2, 4, 8, 16, 31, 32, 64, 103, 128, 171, 213, 256, 301, 342, 439, 475, 494, 512, 558
Offset: 1

Views

Author

Keywords

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

Views

Author

Keywords

References

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

Crossrefs

Cf. A000069, A054016, A054043, etc.

Programs

  • Mathematica
    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 *)

Formula

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

Extensions

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

A054043 Grundy function for turn-at-most-6-coins game.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 63, 64, 128, 256, 455, 512, 729, 874, 948, 1024, 1259, 1393, 1437, 1660, 1678, 1831, 2002, 2048, 4096, 8192, 14343, 16384, 22553, 26666, 28724, 32768, 38955, 43057, 45085, 51260, 53262, 57383, 63506, 65536, 71873
Offset: 1

Author

N. J. A. Sloane, Apr 29 2000

Keywords

References

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

Crossrefs

A054044 Grundy function for turn-at-most-7-coins game.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 127, 128, 256, 512, 911, 1024, 1459, 1749, 1897, 2048, 2518, 2787, 2874, 3320, 3357, 3662, 4004, 4096, 8192, 16384, 28687, 32768, 45107, 53333, 57449, 65536, 77910, 86115, 90170, 102520, 106525, 114766, 127012
Offset: 1

Author

N. J. A. Sloane, Apr 29 2000

Keywords

References

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

Crossrefs

A140460 a(0) = 2; thereafter a(n) = smallest integer not a multiple of an earlier terms nor a sum of two earlier terms.

Original entry on oeis.org

2, 3, 7, 11, 17, 23, 29, 37, 41, 47, 53, 59, 65, 71, 79, 83, 89, 95, 101, 107, 113, 125, 131, 137, 149, 155, 163, 167, 173, 179, 191, 197, 211, 215, 223, 227, 233, 239, 247, 251, 257, 263, 269, 277, 281, 293, 305, 311, 317, 331, 335
Offset: 0

Author

Russell Y. Webb (r.webb(AT)elec.canterbury.ac.nz), Jul 22 2008

Keywords

Comments

Note that the first composite value is a(12) = 65 = 5 * 13, since 5 and 13 are the first two primes sieved out of the sequence. Similarly, the second composite value is a(17) = 95 = 5 * 19, since 5 and 19 are the first and third primes sieved out of the sequence. - Jonathan Vos Post, Jul 27 2008

Programs

  • C
    #include 
    #include 
    void sieve(){ const int first = 2; const int max = 10000; bool member[max]; for(int i = first; i < max; ++i){ member[i] = true; } for(int i = first; i < max; ++i){ if(member[i]){ for(int x = i + i; x < max; x += i){ member[x] = false; } for(int j = first; j < i; ++j){ if(member[j] && i + j < max){ member[i + j] = false; } } } } int num = 0; for(int i = first; i < max; ++i){ if(member[i]){ printf("%i, ", i); num += 1; } } printf(" num = %i ", num); }
  • Mathematica
    s={2};Do[m=2;Until[Total[Boole[Divisible[m,s]]]==0&&!MemberQ[Total/@Subsets[s,{2}],m],m++];AppendTo[s,m],{n,50}];s (* James C. McMahon, Jul 09 2025 *)

A054045 Grundy function for turn-at-most-8-coins game.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 128, 255, 256, 512, 1024, 2048, 3855, 4096, 8192, 13107, 16384, 21845, 27306, 32768, 38506, 65536, 71576, 92115, 101470, 131072, 138406, 172589, 240014, 262144, 272069, 380556, 524288, 536169, 679601
Offset: 1

Author

N. J. A. Sloane, Apr 29 2000

Keywords

References

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

Crossrefs

A054046 Grundy function for turn-at-most-9-coins game.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 512, 1024, 2048, 4096, 7711, 8192, 16384, 26215, 32768, 43691, 54613, 65536, 77013, 131072, 143153, 184230, 202940, 262144, 276813, 345179, 480029, 524288, 544139, 761113, 1048576, 1072338
Offset: 1

Author

N. J. A. Sloane, Apr 29 2000

Keywords

References

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

Crossrefs

Showing 1-7 of 7 results.