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 1-9 of 9 results.

A026414 a(n) = greatest integer not found after first n in A026409.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 24, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27
Offset: 2

Views

Author

Clark Kimberling

Keywords

Extensions

More terms from Sean A. Irvine, Sep 26 2019

A026407 a(n) = greatest k such that s(j) > 0 for all j < k at end of stage n in forming A026409.

Original entry on oeis.org

1, 2, 4, 6, 7, 10, 12, 15, 19, 23, 28, 31, 36, 37, 45, 49, 58, 60, 67, 75, 77, 90, 91, 104, 110, 111, 125, 135, 145, 158, 160, 163, 186, 202, 203, 218, 219, 236, 254, 256, 274, 283, 303, 322, 325, 353, 358, 359, 390, 405, 407, 448, 450, 477, 492, 494, 498, 543, 544, 547, 587, 589
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A026409.

Extensions

More terms from Sean A. Irvine, Sep 26 2019

A026408 a(n) = s(k), where, at the end of stage n when forming A026409, k is the greatest integer such that s(j) > 0 for all j < k.

Original entry on oeis.org

1, 2, 2, 3, 5, 4, 5, 6, 7, 8, 6, 8, 11, 14, 13, 11, 13, 11, 17, 13, 18, 20, 23, 17, 20, 26, 24, 25, 27, 28, 25, 21, 28, 27, 35, 30, 37, 24, 26, 37, 34, 39, 41, 39, 36, 22, 26, 48, 46, 47, 48, 33, 34, 52, 46, 31, 32, 38, 59, 50, 36, 31, 33, 55, 64, 66, 67, 68, 65, 58, 59, 72, 65
Offset: 1

Views

Author

Clark Kimberling

Keywords

Extensions

More terms from Sean A. Irvine, Sep 26 2019

A026410 a(n) = position of the first n in A026409.

Original entry on oeis.org

1, 2, 3, 5, 7, 8, 11, 13, 16, 20, 24, 29, 32, 37, 38, 46, 50, 59, 61, 68, 76, 78, 91, 92, 105, 111, 112, 126, 136, 146, 159, 161, 164, 187, 203, 204, 219, 220, 237, 255, 257, 275, 284, 304, 323, 326, 354, 359, 360, 391, 406, 408, 449, 451, 478, 493, 495, 499, 544, 545, 548, 588
Offset: 1

Views

Author

Clark Kimberling

Keywords

Extensions

Corrected and extended by Sean A. Irvine, Sep 26 2019

A026411 Position of the second n in A026409.

Original entry on oeis.org

4, 6, 10, 12, 15, 19, 23, 25, 30, 36, 43, 45, 51, 54, 66, 67, 77, 87, 90, 99, 100, 124, 125, 135, 139, 145, 158, 178, 180, 196, 197, 201, 225, 241, 252, 256, 258, 283, 302, 303, 321, 327, 350, 383, 390, 405, 407, 426, 447, 459, 477, 520, 523, 542, 568, 569, 586, 611, 614, 615
Offset: 2

Views

Author

Clark Kimberling

Keywords

Extensions

More terms from Sean A. Irvine, Sep 26 2019

A026412 a(n) = position of the n-th n in A026409.

Original entry on oeis.org

1, 4, 9, 18, 27, 40, 55, 72, 89, 113, 140, 167, 194, 221, 253, 294, 329, 369, 419, 452, 502, 552, 618, 677, 721, 776, 836, 894, 976, 1049, 1121, 1175, 1248, 1348, 1415, 1489, 1574, 1658, 1756, 1845, 1925, 2037, 2122, 2224, 2356, 2442, 2551, 2635, 2762, 2875, 3000
Offset: 1

Views

Author

Clark Kimberling

Keywords

Extensions

More terms from Sean A. Irvine, Sep 26 2019

A026413 a(n) = greatest number of numbers between consecutive appearances of n in A026409.

Original entry on oeis.org

1, 2, 4, 4, 6, 7, 9, 9, 11, 13, 13, 16, 15, 15, 19, 19, 19, 25, 21, 22, 27, 32, 32, 29, 34, 32, 31, 41, 37, 36, 36, 37, 48, 40, 47, 43, 44, 45, 46, 45, 51, 50, 49, 59, 63, 51, 51, 65, 55, 59, 69, 70, 71, 68, 74, 73, 86, 68, 74, 75, 85, 82, 90, 95, 77, 79, 83, 82, 80, 79, 89, 90
Offset: 2

Views

Author

Clark Kimberling

Keywords

Extensions

More terms from Sean A. Irvine, Sep 26 2019

A026415 Numbers k such that A026409(k) is odd.

Original entry on oeis.org

1, 3, 6, 7, 9, 11, 12, 16, 17, 19, 22, 24, 25, 26, 27, 32, 33, 35, 36, 38, 41, 44, 45, 48, 49, 50, 53, 54, 55, 58, 60, 61, 62, 67, 70, 71, 74, 75, 76, 80, 84, 85, 86, 87, 88, 89, 91, 96, 99, 101, 102, 104, 105, 107, 108, 112, 114, 117, 118, 120, 121, 124, 127, 128, 129, 132
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A026409.

Extensions

More terms from Sean A. Irvine, Sep 26 2019

A077113 Number of nonnegative integer cubes <= n^2.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19
Offset: 0

Views

Author

Reinhard Zumkeller, Oct 29 2002

Keywords

Comments

a(n) is the least number m such that m^3 > n^2. - Zak Seidov, May 03 2005

Examples

			Cubes <= 10^2: 0, 1, 8, 27 and 64, hence a(10) = 5.

Links

Crossrefs

Cf. A026409, A026414, A054071, A077106, A077121, A100196.

Programs

  • Mathematica
    Table[Floor[n^(2/3) + 1], {n, 0, 100}] (* Zak Seidov, May 03 2005 *)
  • Python
    from sympy import integer_nthroot
def A077113(n): return integer_nthroot(n**2,3)[0]+1 # Chai Wah Wu, Aug 15 2025

Formula

a(n) = floor(n^(2/3))+1.
a(n) = [x^(n^2)] (1/(1 - x))*Sum_{k>=0} x^(k^3). - Ilya Gutkovskiy, Apr 20 2018
a(n) = A100196(n) + 1. - Amiram Eldar, Apr 05 2025

Extensions

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar
Showing 1-9 of 9 results.

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

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