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 11 results. Next

A163172 Maxima in A163169.

Original entry on oeis.org

0, 1, 6, 10, 20, 28, 44, 88, 104, 136, 272, 304, 368, 464, 496, 592, 1184, 1312, 1376, 1504, 1696, 1888, 1952, 2144, 4288, 4544, 4672, 5056, 5312, 5696, 6208, 6464, 6592, 6848, 6976, 7232, 8128, 8384, 16768, 17536, 17792, 19072, 19328, 20096, 20864
Offset: 1

Views

Author

Carl R. White, Jul 22 2009, Jul 23 2009

Keywords

Links

Crossrefs

Cf. A163169, A138591, A057716.

A270298 Numbers which are representable as a sum of eight but no fewer consecutive nonnegative integers.

Original entry on oeis.org

44, 52, 68, 76, 92, 116, 124, 148, 164, 172, 188, 212, 236, 244, 268, 284, 292, 316, 332, 356, 388, 404, 412, 428, 436, 452, 484, 508, 524, 548, 556, 572, 596, 604, 628, 652, 668, 676, 692, 716, 724, 748, 764, 772, 788, 796, 836, 844, 884, 892, 908, 916, 932
Offset: 1

Views

Author

Martin Renner, Mar 14 2016

Keywords

Examples

			36 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 11 + 12 + 13 (not in sequence);
44 = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9;
52 = 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10;
68 = 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12.

Links

Crossrefs

Cf. A008364, A138591, A270296, A270297, A270299, A270300, A270301, A270302, A270303.

Formula

A163169(a(n)) = 8. - Ray Chandler, Mar 22 2016
a(n) = 4*A008364(n+1). - Hugo Pfoertner, Feb 04 2021

A270301 Numbers which are representable as a sum of sixteen but no fewer consecutive nonnegative integers.

Original entry on oeis.org

136, 152, 184, 232, 248, 296, 328, 344, 376, 424, 472, 488, 536, 568, 584, 632, 664, 712, 776, 808, 824, 856, 872, 904, 1016, 1048, 1096, 1112, 1192, 1208, 1256, 1304, 1336, 1384, 1432, 1448, 1528, 1544, 1576, 1592, 1688, 1784, 1816, 1832, 1864, 1912, 1928
Offset: 1

Views

Author

Martin Renner, Mar 14 2016

Keywords

Examples

			136 = 1 + 2 + 3 + ... + 14 + 15 + 16;
152 = 2 + 3 + 4 + ... + 15 + 16 + 17;
169 = 3 + 4 + 5 + ... + 16 + 17 + 18 = 84 + 85 (not in sequence);
184 = 4 + 5 + 6 + ... + 17 + 18 + 19.

Links

Crossrefs

Cf. A138591, A270296, A270297, A270298, A270299, A270300, A270302, A270303.

Formula

A163169(a(n)) = 16. - Ray Chandler, Mar 22 2016
a(n) == 0 (mod 8). - Hugo Pfoertner, Feb 04 2021

A270296 Numbers which are representable as a sum of five but no fewer consecutive nonnegative integers.

Original entry on oeis.org

20, 40, 80, 100, 140, 160, 200, 220, 260, 280, 320, 340, 380, 400, 440, 460, 500, 520, 560, 580, 620, 640, 680, 700, 740, 760, 800, 820, 860, 880, 920, 940, 980, 1000, 1040, 1060, 1100, 1120, 1160, 1180, 1220, 1240, 1280, 1300, 1340, 1360, 1400, 1420, 1460
Offset: 1

Views

Author

Martin Renner, Mar 14 2016

Keywords

Examples

			15 = 1 + 2 + 3 + 4 + 5 = 7 + 8 (not in sequence);
20 = 2 + 3 + 4 + 5 + 6;
40 = 6 + 7 + 8 + 9 + 10;
80 = 14 + 15 + 16 + 17 + 18.

Links

Crossrefs

Cf. A001651, A138591, A270297, A270298, A270299, A270300, A270301, A270302, A270303.

Formula

A163169(a(n)) = 5. - Ray Chandler, Mar 22 2016
a(n) = 20*A001651(n). - Hugo Pfoertner, Feb 04 2021

A270303 Numbers which are representable as a sum of nineteen but no fewer consecutive nonnegative integers.

Original entry on oeis.org

304, 608, 1216, 2432, 4864, 5776, 6992, 8816, 9424, 9728, 11248, 11552, 12464, 13072, 13984, 14288, 16112, 17632, 17936, 18544, 18848, 19456, 20368, 21584, 22192, 22496, 23104, 24016, 24928, 25232, 26144, 27056, 27968, 28576, 29488, 30704, 31312, 32224, 32528
Offset: 1

Views

Author

Martin Renner, Mar 14 2016

Keywords

Examples

			190 = 1 + 2 + 3 + ... + 17 + 18 + 19 = 46 + 47 + 48 + 49 (not in sequence);
304 = 7 + 8 + 9 + ... + 23 + 24 + 25;
608 = 23 + 24 + 25 + ... + 39 + 40 + 41;
1216 = 55 + 56 + 57 + ... + 71 + 72 + 73.

Links

Crossrefs

Cf. A138591, A270296, A270297, A270298, A270299, A270300, A270301, A270302.

Formula

A163169(a(n)) = 19. - Ray Chandler, Mar 22 2016
a(n) == 0 (mod 304). - Hugo Pfoertner, Feb 04 2021

A270297 Numbers which are representable as a sum of seven but no fewer consecutive nonnegative integers.

Original entry on oeis.org

28, 56, 112, 196, 224, 308, 364, 392, 448, 476, 532, 616, 644, 728, 784, 812, 868, 896, 952, 1036, 1064, 1148, 1204, 1232, 1288, 1316, 1372, 1456, 1484, 1568, 1624, 1652, 1708, 1736, 1792, 1876, 1904, 1988, 2044, 2072, 2128, 2156, 2212, 2296, 2324, 2408, 2464
Offset: 1

Views

Author

Martin Renner, Mar 14 2016

Keywords

Examples

			28 = 1 + 2 + 3 + 4 + 5 + 6 + 7;
35 = 2 + 3 + 4 + 5 + 6 + 7 + 8 = 17 + 18 (not in sequence);
56 = 5 + 6 + 7 + 8 + 9 + 10 + 11;
112 = 13 + 14 + 15 + 16 + 17 + 18 + 19.

Links

Crossrefs

Cf. A138591, A229829, A270296, A270298, A270299, A270300, A270301, A270302, A270303.

Formula

A163169(a(n)) = 7. - Ray Chandler, Mar 22 2016
a(n) = 28*A229829(n). - Hugo Pfoertner, Feb 04 2021

A270299 Numbers which are representable as a sum of eleven but no fewer consecutive nonnegative integers.

Original entry on oeis.org

88, 176, 352, 704, 968, 1144, 1408, 1496, 1672, 1936, 2024, 2288, 2552, 2728, 2816, 2992, 3256, 3344, 3608, 3784, 3872, 4048, 4136, 4576, 4664, 5104, 5192, 5368, 5456, 5632, 5896, 5984, 6248, 6424, 6512, 6688, 6952, 7216, 7304, 7568, 7744, 7832, 8096, 8272
Offset: 1

Views

Author

Martin Renner, Mar 14 2016

Keywords

Examples

			66 = 1 + 2 + 3 + ... + 9 + 10 + 11 = 21 + 22 + 23 (not in sequence);
88 = 3 + 4 + 5 + ... + 11 + 12 + 13;
176 = 11 + 12 + 13 + ... + 19 + 20 + 21;
352 = 27 + 28 + 29 + ... + 35 + 36 + 37.

Links

Crossrefs

Cf. A138591, A236206, A270296, A270297, A270298, A270300, A270301, A270302, A270303.

Formula

A163169(a(n)) = 11. - Ray Chandler, Mar 22 2016
a(n) = 88*A236206(n). - Hugo Pfoertner, Feb 04 2021

A270300 Numbers which are representable as a sum of thirteen but no fewer consecutive nonnegative integers.

Original entry on oeis.org

104, 208, 416, 832, 1352, 1664, 1768, 1976, 2392, 2704, 3016, 3224, 3328, 3536, 3848, 3952, 4264, 4472, 4784, 4888, 5408, 5512, 6032, 6136, 6344, 6448, 6656, 6968, 7072, 7384, 7592, 7696, 7904, 8216, 8528, 8632, 8944, 9256, 9568, 9776, 10088, 10504, 10712
Offset: 1

Views

Author

Martin Renner, Mar 14 2016

Keywords

Examples

			90 = 1 + 2 + 3 + ... + 11 + 12 + 13 = 29 + 30 + 31 (not in sequence);
104 = 2 + 3 + 4 + ... + 12 + 13 + 14;
208 = 10 + 11 + 12 + ... + 20 + 21 + 22;
416 = 26 + 27 + 28 + ... + 36 + 37 + 38.

Links

Crossrefs

Cf. A138591, A270296, A270297, A270298, A270299, A270301, A270302, A270303.

Formula

A163169(a(n)) = 13. - Ray Chandler, Mar 22 2016
a(n) == 0 (mod 104). - Hugo Pfoertner, Feb 04 2021

A270302 Numbers which are representable as a sum of seventeen but no fewer consecutive nonnegative integers.

Original entry on oeis.org

272, 544, 1088, 2176, 4352, 4624, 5168, 6256, 7888, 8432, 8704, 9248, 10064, 10336, 11152, 11696, 12512, 12784, 14416, 15776, 16048, 16592, 16864, 17408, 18224, 18496, 19312, 19856, 20128, 20672, 21488, 22304, 22576, 23392, 24208, 25024, 25568, 26384, 27472
Offset: 1

Views

Author

Martin Renner, Mar 14 2016

Keywords

Examples

			153 = 1 + 2 + 3 + ... + 15 + 16 + 17 = 76 + 77 (not in sequence);
272 = 8 + 9 + 10 + ... + 22 + 23 + 24;
544 = 24 + 25 + 26 + ... + 38 + 39 + 40;
1088 = 56 + 57 + 58 + ... + 70 + 71 + 72.

Crossrefs

Cf. A138591, A270296, A270297, A270298, A270299, A270300, A270301, A270303.

Formula

A163169(a(n)) = 17. - Ray Chandler, Mar 22 2016
a(n) == 0 (mod 272). Hugo Pfoertner, Feb 04 2021

A104514 a(n) = least number k > 1 of consecutive integers which sum to 2*n; or a(n) = 0 if n is a power of 2.

Original entry on oeis.org

0, 0, 3, 0, 4, 3, 4, 0, 3, 5, 4, 3, 4, 7, 3, 0, 4, 3, 4, 5, 3, 8, 4, 3, 4, 8, 3, 7, 4, 3, 4, 0, 3, 8, 4, 3, 4, 8, 3, 5, 4, 3, 4, 11, 3, 8, 4, 3, 4, 5, 3, 13, 4, 3, 4, 7, 3, 8, 4, 3, 4, 8, 3, 0, 4, 3, 4, 16, 3, 5, 4, 3, 4, 8, 3, 16, 4, 3, 4, 5, 3, 8, 4, 3, 4, 8, 3, 11, 4, 3, 4, 16, 3, 8, 4, 3, 4, 7, 3, 5, 4, 3, 4
Offset: 1

Views

Author

Alfred S. Posamentier (asp2(AT)juno.com) and Robert G. Wilson v, Feb 23 2005

Keywords

Comments

a(2^k) = 0 and a(3*n) = 3.
Least proper divisor d of 4*n (if any) such that d or 4*n/d is odd. - Robert Israel, May 06 2015

Examples

			a(9) = 3 because 3+4+5+6 = 5+6+7 = 2*9 = 18.

References

  • Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 67.

Links

Crossrefs

Cf. A104512, A104513, A104515, A104516, A163169.

Programs

  • Maple
    a:= proc(n) local divs,r;
   divs:= select(t -> t::odd or (4*n/t)::odd, numtheory:-divisors(4*n) minus {1,4*n});
   if nops(divs)=0 then 0 else min(divs) fi
end proc:
seq(a(n), n=1..200); # Robert Israel, May 06 2015
  • Mathematica
    f[n_] := Block[{r = Ceiling[n/2]}, If[IntegerQ[Log[2, n]], 0, m = Range[r]; lst = Flatten[Table[m[[k]], {i, r}, {j, i + 1, r}, {k, i, j}], 1]; Min[Length /@ lst[[Flatten[Position[Plus @@@ lst, n]]]]]]]; Table[f[2n], {n, 103}]

Formula

a(n) = A163169(2*n). Robert Israel, May 06 2015
Showing 1-10 of 11 results. Next

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