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 1-10 of 28 results. Next

A113743 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 6 multiples of n-1, n-2, ..., 1.

Original entry on oeis.org

1, 7, 19, 37, 61, 87, 123, 163, 207, 253, 307, 373, 447, 511, 589, 673, 763, 843, 949, 1087, 1179, 1309, 1393, 1531, 1693, 1807, 1933, 2119, 2263, 2439, 2559, 2761, 2967, 3147, 3327, 3499, 3691, 3883, 4123, 4309, 4603, 4783, 5067, 5209, 5539, 5763, 6013
Offset: 1

Views

Author

Paul D. Hanna, Oct 12 2005

Keywords

Examples

			a(1)=1: 1;
a(2)=7: 2->7;
a(3)=19: 3->14->19;
a(4)=37: 4->21->32->37;
a(5)=61: 5->28->45->56->61;
a(6)=87: 6->35->56->72->82->87;
a(7)=123: 7->42->70->92->108->118->123;
a(8)=163: 8->49->84->110->132->147->158->163;
a(9)=207: 9->56->91->126->155->176->192->202->207;
a(10)=253: 10->63->104->140->174->200->220->237->248->253.

Links

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; det. A113749.
Cf. A002491, A000960, A112557, A112558.

Programs

  • Mathematica
    f[n_] := Fold[ #2*Ceiling[ #1/#2 + 5] &, n, Reverse@Range[n - 1]]; Array[f, 47]
  • PARI
    a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+5));A

Formula

a(4*n-3) = A112558(5*n-4), a(8*n-7) = A000960(15*n-14), for n>=1.

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 31 2007

A113744 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 7 multiples of n-1, n-2, ..., 1, for n>=1.

Original entry on oeis.org

1, 8, 22, 42, 70, 102, 142, 192, 240, 298, 360, 438, 510, 612, 708, 780, 898, 1002, 1122, 1254, 1392, 1542, 1662, 1834, 1992, 2118, 2302, 2494, 2662, 2862, 3054, 3274, 3502, 3648, 3930, 4114, 4374, 4582, 4834, 5122, 5382, 5628, 5938, 6162, 6462, 6834, 7092
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Nov 05 2005

Keywords

Links

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; det. A113749.

Programs

  • Mathematica
    f[n_] := Fold[ #2*Ceiling[ #1/#2 + 6] &, n, Reverse@Range[n - 1]]; Array[f, 47]

A113746 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 9 multiples of n-1, n-2, ..., 1, for n>=1.

Original entry on oeis.org

1, 10, 28, 54, 90, 132, 180, 240, 318, 394, 480, 570, 672, 778, 898, 1042, 1174, 1332, 1474, 1632, 1812, 1992, 2160, 2340, 2580, 2760, 3018, 3252, 3502, 3720, 3972, 4222, 4498, 4818, 5118, 5382, 5718, 6022, 6378, 6672, 7038, 7378, 7714, 8112, 8430, 8850
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Nov 05 2005

Keywords

Links

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; det. A113749.

Programs

  • Mathematica
    f[n_] := Fold[ #2*Ceiling[ #1/#2 + 8] &, n, Reverse@Range[n - 1]]; Array[f, 46]

A113749 Consider the generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next k multiples of n-1, n-2, ..., 1, for n>=1. Now construct the array, t, such that t(n,k) is the n-th and successively rounding up to the next k multiples. This sequence is the presentation of that array by reading the antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 7, 6, 1, 1, 5, 10, 13, 10, 1, 1, 6, 13, 18, 19, 12, 1, 1, 7, 16, 25, 30, 27, 18, 1, 1, 8, 19, 30, 39, 42, 39, 22, 1, 1, 9, 22, 37, 48, 61, 58, 49, 30, 1, 1, 10, 25, 42, 61, 72, 79, 78, 63, 34, 1, 1, 11, 28, 49, 70, 87, 102, 103, 102, 79, 42, 1, 1, 12, 31
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Nov 05 2005

Keywords

Comments

The determinant of t(i,j), i=1..n, j=1..n, n=1..inf. is: 1,1,0,0,0,0, ...,.
The determinant of t(i,j), i=1..n, j=-1..n-2, n=1..inf. is: 1,1,0,0,0,0, ...,.

Examples

			1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...,.
1, 2, 4, 6, 10, 12, 18, 22, 30, 34, 42, 48, 58, 60, 78, ...,.
1, 3, 7, 13, 19, 27, 39, 49, 63, 79, 91, 109, 133, 147, 181, ...,.
1, 4, 10, 18, 30, 42, 58, 78, 102, 118, 150, 174, 210, 240, 274, ...,.
1, 5, 13, 25, 39, 61, 79, 103, 133, 169, 207, 241, 289, 331, 387, ...,.
1, 6, 16, 30, 48, 72, 102, 132, 168, 210, 258, 318, 360, 418, 492, ...,.
1, 7, 19, 37, 61, 87, 123, 163, 207, 253, 307, 373, 447, 511, 589, ...,.
1, 8, 22, 42, 70, 102, 142, 192, 240, 298, 360, 438, 510, 612, 708, ...,.
1, 9, 25, 49, 79, 121, 163, 219, 279, 349, 423, 507, 589, 687, 807, ...,.
1, 10, 28, 54, 90, 132, 180, 240, 318, 394, 480, 570, 672, 778, 898, ...,.
1, 11, 31, 61, 99, 147, 207, 271, 349, 439, 529, 643, 751, 867,1009, ...,.
1, 12, 34, 66, 108, 162, 228, 298, 382, 480, 588, 708, 838, 972,1114, ...,.

Links

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748.

Programs

  • Mathematica
    f[n_, k_] := Fold[ #2*Ceiling[ #1/#2 + k] &, n, Reverse@Range[n - 1]]; Table[f[n - k + 1, k], {n, -1, 11}, {k, n, -1, -1}] // Flatten

A112557 Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire which make use of (2*n-1)-th hole for n>=1; a bisection of A002491.

Original entry on oeis.org

1, 4, 10, 18, 30, 42, 58, 78, 102, 118, 150, 174, 210, 240, 274, 322, 360, 402, 442, 498, 540, 612, 648, 718, 780, 840, 918, 990, 1054, 1122, 1200, 1278, 1392, 1428, 1548, 1632, 1714, 1834, 1882, 2040, 2118, 2242, 2314, 2434, 2580, 2662, 2760, 2922, 3054
Offset: 1

Views

Author

Paul D. Hanna, Oct 10 2005

Keywords

Examples

			To get 10th term: 10->36->56->70->84->95->104->111->116->118.
To get 5th term: 5->16->24->28->30; since a(5) = A002491(9), compare with process used by A002491:
A002491(9) = 9->16->21->24->25->28->30->30->30.

Links

Crossrefs

Cf. A000012, A002491, A000960 (Flavius Josephus's sieve), A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; A113749.

Programs

  • Mathematica
    f[n_] := Fold[ #2 * Ceiling[ #1/#2 + 2] &, n, Reverse @ Range[n - 1]]; Array[ f, 49] (* Bobby R. Treat (drbob(at)bigfoot.com), Oct 11 2005 *)
  • PARI
    a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+2));A

Formula

To get n-th term, start with n and successively round up to next 3 multiples of n-1, n-2, ..., 1 (compare to method used by A002491). Surprisingly, a(n) = A002491(2*n-1).

A112558 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 4 multiples of n-1, n-2, ..., 1, for n>=1.

Original entry on oeis.org

1, 5, 13, 25, 39, 61, 79, 103, 133, 169, 207, 241, 289, 331, 387, 447, 481, 553, 613, 687, 763, 819, 927, 979, 1093, 1179, 1261, 1347, 1471, 1539, 1693, 1759, 1899, 2019, 2161, 2263, 2367, 2527, 2703, 2779, 2967, 3073, 3199, 3373, 3529, 3691, 3841, 3987, 4203
Offset: 1

Views

Author

Paul D. Hanna, Oct 12 2005

Keywords

Examples

			a(1)=1: 1;
a(2)=5: 2->5;
a(3)=13: 3->10->13;
a(4)=25: 4->15->22->25;
a(5)=39: 5->20->30->36->39;
a(6)=61: 6->25->40->51->58->61;
a(7)=79: 7->30->45->60->69->76->79;
a(8)=103: 8->35->54->70->84->93->100->103;
a(9)=133: 9->40->63->84->100->112->123->130->133;
a(10)=169: 10->45->72->98->120->135->148->159->166->169.

Links

Crossrefs

Cf. A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A113742, A113743, A113744, A113745, A113746, A113747, A113748; A113749.

Programs

  • Mathematica
    f[n_] := Fold[#2*Ceiling[#1/#2 + 3] &, n, Reverse@ Range[n - 1]]; Array[f, 49]
  • PARI
    a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+3));A

Formula

a(2*n-1) = A000960(3*n-2), where A000960 is Flavius Josephus's sieve.

A113742 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 5 multiples of n-1, n-2, ..., 1, for n>=1.

Original entry on oeis.org

1, 6, 16, 30, 48, 72, 102, 132, 168, 210, 258, 318, 360, 418, 492, 540, 622, 714, 780, 870, 972, 1054, 1174, 1260, 1392, 1488, 1590, 1714, 1848, 2022, 2118, 2292, 2398, 2580, 2718, 2878, 3054, 3234, 3360, 3570, 3754, 3948, 4114, 4318, 4498, 4710, 4932
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Nov 05 2005

Keywords

Links

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113743, A113744, A113745, A113746, A113747, A113748; det. A113749.

Programs

  • Mathematica
    f[n_] := Fold[ #2*Ceiling[ #1/#2 + 4] &, n, Reverse@Range[n - 1]]; Array[f, 47]

A113745 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 8 multiples of n-1, n-2, ..., 1, for n>=1.

Original entry on oeis.org

1, 9, 25, 49, 79, 121, 163, 219, 279, 349, 423, 507, 589, 687, 807, 927, 1027, 1171, 1309, 1453, 1579, 1743, 1909, 2101, 2263, 2479, 2703, 2851, 3073, 3279, 3499, 3807, 3973, 4239, 4543, 4767, 5067, 5293, 5563, 5893, 6159, 6547, 6799, 7189, 7419, 7839
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Nov 05 2005

Keywords

Links

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113746, A113747, A113748, A113749.

Programs

  • Mathematica
    f[n_] := Fold[ #2*Ceiling[ #1/#2 + 7] &, n, Reverse@Range[n - 1]]; Array[f, 46]

A113747 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 10 multiples of n-1, n-2, ..., 1, for n>=1.

Original entry on oeis.org

1, 11, 31, 61, 99, 147, 207, 271, 349, 439, 529, 643, 751, 867, 1009, 1143, 1309, 1471, 1651, 1807, 2019, 2223, 2439, 2629, 2851, 3109, 3363, 3619, 3879, 4179, 4429, 4759, 5067, 5329, 5667, 6013, 6387, 6723, 7069, 7407, 7839, 8283, 8593, 9039, 9423, 9889
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Nov 05 2005

Keywords

Links

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113748, A113749.

Programs

  • Mathematica
    f[n_] := Fold[ #2*Ceiling[ #1/#2 + 9] &, n, Reverse@Range[n - 1]]; Array[f, 46]

A113748 Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 11 multiples of n-1, n-2, ..., 1, for n>=1.

Original entry on oeis.org

1, 12, 34, 66, 108, 162, 228, 298, 382, 480, 588, 708, 838, 972, 1114, 1260, 1428, 1620, 1812, 2022, 2242, 2434, 2662, 2922, 3228, 3394, 3702, 3972, 4302, 4578, 4908, 5254, 5610, 5938, 6318, 6658, 7038, 7452, 7800, 8262, 8688, 9058, 9480, 9990, 10474
Offset: 1

Views

Author

Paul D. Hanna and Robert G. Wilson v, Nov 05 2005

Keywords

Links

Crossrefs

Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113749.

Programs

  • Mathematica
    f[n_] := Fold[ #2*Ceiling[ #1/#2 + 10] &, n, Reverse@Range[n - 1]]; Array[f, 46]
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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