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.

Previous Showing 11-20 of 24 results. Next

A004921 a(n) = floor(n*phi^6), phi = golden ratio, A001622.

Original entry on oeis.org

0, 17, 35, 53, 71, 89, 107, 125, 143, 161, 179, 197, 215, 233, 251, 269, 287, 305, 322, 340, 358, 376, 394, 412, 430, 448, 466, 484, 502, 520, 538, 556, 574, 592, 610, 628, 645, 663, 681, 699, 717, 735, 753, 771
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004922, A004923, A004924, A004925, A004926.
Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622, A098317.

Programs

  • Magma
    [Floor((9+4*Sqrt(5))*n): n in [0..50]]; // G. C. Greubel, Aug 22 2023
  • Mathematica
    Floor[GoldenRatio^6*Range[0, 50]] (* G. C. Greubel, Aug 22 2023 *)
  • SageMath
    [floor((9+4*sqrt(5))*n) for n in range(51)] # G. C. Greubel, Aug 22 2023

Formula

From G. C. Greubel, Aug 22 2023: (Start)
a(n) = floor((9 + 4*sqrt(5))*n).
a(n) = floor((A098317)^2*n). (End)

A004923 a(n) = floor(n*phi^8), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 46, 93, 140, 187, 234, 281, 328, 375, 422, 469, 516, 563, 610, 657, 704, 751, 798, 845, 892, 939, 986, 1033, 1080, 1127, 1174, 1221, 1268, 1315, 1362, 1409, 1456, 1503, 1550, 1597, 1644, 1691, 1738, 1785
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004924, A004925, A004926.
Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((47+21*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Aug 24 2023
  • Mathematica
    With[{c=GoldenRatio^8},Floor[c*Range[0,40]]] (* Harvey P. Dale, Sep 08 2020 *)
  • SageMath
    [floor(golden_ratio^8*n) for n in range(61)] # G. C. Greubel, Aug 24 2023

A004925 a(n) = floor(n*phi^10), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 122, 245, 368, 491, 614, 737, 860, 983, 1106, 1229, 1352, 1475, 1598, 1721, 1844, 1967, 2090, 2213, 2336, 2459, 2582, 2705, 2828, 2951, 3074, 3197, 3320, 3443, 3566, 3689, 3812, 3935, 4058, 4181
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004926.
Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622 (phi).

Programs

  • Magma
    [Floor((123+55*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Aug 27 2023
  • Maple
    A004925:=n->floor(n*((1 + sqrt(5))/2)^10): seq(A004925(n), n=0..100); # Wesley Ivan Hurt, Jul 26 2017
  • Mathematica
    Floor[GoldenRatio^(10)*Range[0,60]] (* G. C. Greubel, Aug 27 2023 *)
  • SageMath
    [floor(golden_ratio^(10)*n) for n in range(61)] # G. C. Greubel, Aug 27 2023

A004927 a(n) = floor(n*phi^12), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 321, 643, 965, 1287, 1609, 1931, 2253, 2575, 2897, 3219, 3541, 3863, 4185, 4507, 4829, 5151, 5473, 5795, 6117, 6439, 6761, 7083, 7405, 7727, 8049, 8371, 8693, 9015, 9337, 9659, 9981, 10303, 10625
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004928, A004929, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((161+72*Sqrt(5))*n): n in [0..60]]; // G. C. Greubel, Aug 27 2023
  • Mathematica
    Floor[GoldenRatio^(12)*Range[0,60]] (* G. C. Greubel, Aug 27 2023 *)
  • SageMath
    [floor(golden_ratio^(12)*n) for n in range(61)] # G. C. Greubel, Aug 27 2023

A004929 a(n) = floor(n*phi^14), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 842, 1685, 2528, 3371, 4214, 5057, 5900, 6743, 7586, 8429, 9272, 10115, 10958, 11801, 12644, 13487, 14330, 15173, 16016, 16859, 17702, 18545, 19388, 20231, 21074, 21917, 22760, 23603, 24446
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004930, A004931, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((843+377*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Sep 05 2023
  • Mathematica
    Floor[GoldenRatio^(14)*Range[0, 60]] (* G. C. Greubel, Sep 05 2023 *)
  • SageMath
    [floor(golden_ratio^(14)*n) for n in range(61)] # G. C. Greubel, Sep 05 2023

A004931 a(n) = floor(n*phi^16), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 2206, 4413, 6620, 8827, 11034, 13241, 15448, 17655, 19862, 22069, 24276, 26483, 28690, 30897, 33104, 35311, 37518, 39725, 41932, 44139, 46346, 48553, 50760, 52967, 55174, 57381, 59588, 61795
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004929, A004930, A004932, A004933.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((2207+987*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Sep 06 2023
  • Mathematica
    Floor[GoldenRatio^(16)*Range[0, 60]] (* G. C. Greubel, Sep 06 2023 *)
  • SageMath
    [floor(golden_ratio^(16)*n) for n in range(61)] # G. C. Greubel, Sep 06 2023

A004933 a(n) = floor(n*phi^18), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 5777, 11555, 17333, 23111, 28889, 34667, 40445, 46223, 52001, 57779, 63557, 69335, 75113, 80891, 86669, 92447, 98225, 104003, 109781, 115559, 121337, 127115, 132893, 138671, 144449, 150227
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004929, A004930, A004931, A004932.
Cf. A004934, A004935, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((2889+1292*Sqrt(5))*n): n in [0..60]]; // G. C. Greubel, Sep 11 2023
  • Mathematica
    With[{p=GoldenRatio^18},Floor[p*Range[0,30]]] (* Harvey P. Dale, Mar 06 2022 *)
  • SageMath
    [floor(golden_ratio^(18)*n) for n in range(61)] # G. C. Greubel, Sep 11 2023

A004935 a(n) = floor(n*phi^20), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 15126, 30253, 45380, 60507, 75634, 90761, 105888, 121015, 136142, 151269, 166396, 181523, 196650, 211777, 226904, 242031, 257158, 272285, 287412, 302539, 317666, 332793, 347920, 363047, 378174
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

From Joerg Arndt, Sep 12 2023: (Start)
phi^20 = 15126.999933893... is a near integer.
Therefore the (incorrect!) g.f. 1 + (-1 + 15128*x)/(1-x)^2 produces the initial about 15000 terms of this sequence.
(End)

Links

Crossrefs

Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.
Cf. A004926, A004927, A004928, A004929, A004930, A004931, A004932.
Cf. A004933, A004934, A004976, A066096, A090909.
Cf. A001622.

Programs

  • Magma
    [Floor((15127+6765*Sqrt(5))*n/2): n in [0..60]]; // G. C. Greubel, Sep 12 2023
  • Mathematica
    With[{c=GoldenRatio^20},Floor[c Range[0,30]]] (* Harvey P. Dale, Feb 18 2013 *)
  • SageMath
    [floor(golden_ratio^(20)*n) for n in range(61)] # G. C. Greubel, Sep 12 2023

A195819 Multiples of 29.

Original entry on oeis.org

0, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, 377, 406, 435, 464, 493, 522, 551, 580, 609, 638, 667, 696, 725, 754, 783, 812, 841, 870, 899, 928, 957, 986, 1015, 1044, 1073, 1102, 1131, 1160, 1189, 1218, 1247, 1276, 1305, 1334
Offset: 0

Views

Author

Omar E. Pol, Oct 12 2011

Keywords

Comments

Length of hypotenuses on the main diagonal of the Pythagorean spiral whose edges have length A195033 and whose vertices are the numbers A195034, if n >= 1.

Links

Crossrefs

Cf. A004922, A004942, A008605, A010868, A135631, A195033, A195034.

Programs

Formula

a(n) = 29*n.
From Elmo R. Oliveira, Mar 21 2024: (Start)
G.f.: 29*x/(x-1)^2.
E.g.f.: 29*x*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

A004962 a(n) = ceiling(n*phi^7), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 30, 59, 88, 117, 146, 175, 204, 233, 262, 291, 320, 349, 378, 407, 436, 465, 494, 523, 552, 581, 610, 639, 668, 697, 726, 755, 784, 813, 842, 872, 901, 930, 959, 988, 1017, 1046, 1075, 1104, 1133, 1162, 1191, 1220, 1249, 1278, 1307, 1336, 1365, 1394, 1423, 1452, 1481, 1510, 1539, 1568, 1597, 1626, 1655, 1684, 1714
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004922 (floor).

Programs

  • Magma
    [Ceiling(n*((1 + Sqrt(5))/2)^7): n in [0..60]]; // Vincenzo Librandi, Jul 22 2015
  • Mathematica
    Table[Ceiling[n ((1 + Sqrt[5])/2)^7], {n, 0, 60}] (* Vincenzo Librandi, Jul 22 2015 *)
Ceiling[Range[0,60]GoldenRatio^7] (* Harvey P. Dale, Nov 18 2018 *)
  • PARI
    p = (sqrt(5)+1)/2; a(n)=ceil(n*p^7);
vector(66,n,a(n-1)) \\ Joerg Arndt, Oct 18 2014

Extensions

More terms added by Joerg Arndt, Oct 18 2014
Previous Showing 11-20 of 24 results. Next

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

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