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 13 results. Next

A159256 a(0)=131; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).

Original entry on oeis.org

131, 142, 153, 165, 177, 190, 203, 217, 231, 246, 261, 277, 293, 310, 327, 345, 363, 382, 401, 421, 441, 462, 483, 504, 526, 548, 571, 594, 618, 642, 667, 692, 718, 744, 771, 798, 826, 854, 883, 912, 942, 972, 1003, 1034, 1066, 1098, 1131, 1164, 1198
Offset: 0

Views

Author

Philippe Deléham, Apr 07 2009

Keywords

Comments

Row 10 in square array A159016. This sequence contains infinitely many squares.
The squares in the sequence are (A175805(k))^2, k=0,1,2,3,... - Vincenzo Librandi, Dec 05 2010

Links

Crossrefs

Cf. A159016, A002984.

Programs

  • Mathematica
    RecurrenceTable[{a[0]==131,a[n]==a[n-1]+Floor[Sqrt[a[n-1]]]},a,{n,50}] (* Harvey P. Dale, Apr 17 2013 *)
NestList[#+Floor[Sqrt[#]]&,131,50] (* Harvey P. Dale, May 11 2019 *)

A159018 a(0)=5; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.

Original entry on oeis.org

5, 7, 9, 12, 15, 18, 22, 26, 31, 36, 42, 48, 54, 61, 68, 76, 84, 93, 102, 112, 122, 133, 144, 156, 168, 180, 193, 206, 220, 234, 249, 264, 280, 296, 313, 330, 348, 366, 385, 404, 424, 444, 465, 486, 508, 530, 553, 576, 600, 624, 648, 673, 698, 724, 750, 777, 804, 832, 860, 889, 918, 948, 978
Offset: 0

Views

Author

Philippe Deléham, Apr 02 2009

Keywords

Comments

Row 1 in square array A159016.
This sequence contains an infinity of squares. - Philippe Deléham, Apr 04 2009
Intersection of the sequence with A000290 generates A002063. - Vincenzo Librandi, Apr 10 2009, clarified by R. J. Mathar, Dec 03 2010

Links

Crossrefs

Cf. A028392.

Programs

  • Maple
    A:= Array(0..100):
A[0]:= 5:
for n from 1 to 100 do A[n]:= A[n-1]+floor(sqrt(A[n-1])) od:
convert(A,list); # Robert Israel, Nov 26 2020

A159021 a(0)=19; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.

Original entry on oeis.org

19, 23, 27, 32, 37, 43, 49, 56, 63, 70, 78, 86, 95, 104, 114, 124, 135, 146, 158, 170, 183, 196, 210, 224, 238, 253, 268, 284, 300, 317, 334, 352, 370, 389, 408, 428, 448, 469, 490, 512, 534, 557, 580, 604, 628, 653, 678, 704, 730, 757, 784, 812, 840, 868, 897, 926, 956, 986, 1017
Offset: 0

Views

Author

Philippe Deléham, Apr 02 2009

Keywords

Comments

Row 3 in square array A159016.
This sequence contains infinitely many squares. - Philippe Deléham, Apr 04 2009
Conjecture: The squares are of the form (7*2^k)^2 (see A005009). - Vincenzo Librandi, Apr 10 2009

Links

Crossrefs

Cf. A028392, A005009.

Programs

  • Mathematica
    NestList[#+Floor[Sqrt[#]]&,19,60] (* Harvey P. Dale, Jan 04 2013 *)

Extensions

More terms from Vincenzo Librandi, Apr 10 2009

A159022 a(0)=29; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.

Original entry on oeis.org

29, 34, 39, 45, 51, 58, 65, 73, 81, 90, 99, 108, 118, 128, 139, 150, 162, 174, 187, 200, 214, 228, 243, 258, 274, 290, 307, 324, 342, 360, 378, 397, 416, 436, 456, 477, 498, 520, 542, 565, 588, 612, 636, 661, 686, 712, 738, 765, 792, 820, 848, 877, 906, 936, 966, 997, 1028
Offset: 0

Views

Author

Philippe Deléham, Apr 02 2009

Keywords

Comments

Row 4 in square array A159016.
This sequence contains infinitely many squares. - Philippe Deléham, Apr 04 2009
There are 10 squares in the first 10000 terms. - Harvey P. Dale, Aug 26 2019

Links

Crossrefs

Cf. A028392, A005010.

Programs

  • Mathematica
    NestList[#+Floor[Sqrt[#]]&,29,60] (* Harvey P. Dale, Aug 26 2019 *)

Extensions

More terms from Vincenzo Librandi, Apr 10 2009

A159027 a(0)=109; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.

Original entry on oeis.org

109, 119, 129, 140, 151, 163, 175, 188, 201, 215, 229, 244, 259, 275, 291, 308, 325, 343, 361, 380, 399, 418, 438, 458, 479, 500, 522, 544, 567, 590, 614, 638, 663, 688, 714, 740, 767, 794, 822, 850, 879, 908, 938, 968, 999, 1030, 1062, 1094, 1127, 1160, 1194, 1228, 1263, 1298, 1334, 1370, 1407, 1444
Offset: 0

Views

Author

Philippe Deléham, Apr 02 2009

Keywords

Comments

Row 9 in square array A159016.
This sequence contains infinitely many squares. - Philippe Deléham, Apr 04 2009

Links

Crossrefs

Cf. A028392, A110288.

Programs

  • Mathematica
    NestList[#+Floor[Sqrt[#]]&,109,60] (* Harvey P. Dale, May 01 2020 *)

Extensions

More terms from Vincenzo Librandi, Apr 10 2009

A159258 a(0)=155; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).

Original entry on oeis.org

155, 167, 179, 192, 205, 219, 233, 248, 263, 279, 295, 312, 329, 347, 365, 384, 403, 423, 443, 464, 485, 507, 529, 552, 575, 598, 622, 646, 671, 696, 722, 748, 775, 802, 830, 858, 887, 916, 946, 976, 1007, 1038, 1070, 1102, 1135, 1168, 1202, 1236, 1271, 1306
Offset: 0

Views

Author

Philippe Deléham, Apr 07 2009

Keywords

Comments

Row 11 of square array in A159016. This sequence contains infinitely many squares.

Links

Programs

  • Mathematica
    RecurrenceTable[{a[n]==a[n-1] + Floor[Sqrt[a[n-1]]], a[0] == 155}, a, {n, 0, 50}] (* G. C. Greubel, Jun 28 2018 *)

A159263 a(0)=181; for n > 0, a(n) = a(n-1) + floor(sqrt a(n-1)).

Original entry on oeis.org

181, 194, 207, 221, 235, 250, 265, 281, 297, 314, 331, 349, 367, 386, 405, 425, 445, 466, 487, 509, 531, 554, 577, 601, 625, 650, 675, 700, 726, 752, 779, 806, 834, 862, 891, 920, 950, 980, 1011, 1042, 1074, 1106, 1139, 1172, 1206, 1240, 1275, 1310, 1346
Offset: 0

Views

Author

Philippe Deléham, Apr 07 2009

Keywords

Comments

Row 12 in square array A159016. This sequence contains infinitely many squares.

Links

Crossrefs

Cf. A159016.

Programs

  • Mathematica
    RecurrenceTable[{a[n]==a[n-1] + Floor[Sqrt[a[n-1]]], a[0] == 181}, a, {n, 0, 50}] (* G. C. Greubel, Jun 28 2018 *)

A159274 a(0)=209; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).

Original entry on oeis.org

209, 223, 237, 252, 267, 283, 299, 316, 333, 351, 369, 388, 407, 427, 447, 468, 489, 511, 533, 556, 579, 603, 627, 652, 677, 703, 729, 756, 783, 810, 838, 866, 895, 924, 954, 984, 1015, 1046, 1078, 1110, 1143, 1176, 1210, 1244, 1279, 1314, 1350, 1386
Offset: 0

Views

Author

Philippe Deléham, Apr 07 2009

Keywords

Comments

Row 13 in square array A159016. This sequence contains infinitely many squares.
The squares in the sequence are (A175806(k))^2, k = 0,1,2,... [Vincenzo Librandi, Dec 05 2010]

Crossrefs

Cf. A159016, A175806.

Programs

  • Magma
    [n eq 1 select 209 else Self(n-1)+Floor(Sqrt (Self(n-1))):n in [1..30]]; // Marius A. Burtea, Jan 07 2020
  • Mathematica
    NestList[#+Floor[Sqrt[#]]&,209,50] (* Harvey P. Dale, Jun 12 2017 *)

A159020 a(0)=11; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.

Original entry on oeis.org

11, 14, 17, 21, 25, 30, 35, 40, 46, 52, 59, 66, 74, 82, 91, 100, 110, 120, 130, 141, 152, 164, 176, 189, 202, 216, 230, 245, 260, 276, 292, 309, 326, 344, 362, 381, 400, 420, 440, 460, 481, 502, 524, 546, 569
Offset: 0

Views

Author

Philippe Deléham, Apr 02 2009

Keywords

Comments

Row 2 in square array A159016.
This sequence contains an infinite number of squares. - Philippe Deléham, Apr 04 2009
The squares in this sequence are A020714(k)^2, k=0,1,2,.... - Vincenzo Librandi, Apr 20 2009 [clarified by R. J. Mathar, Dec 05 2010]

Crossrefs

Cf. A028392, A020714.

A159023 a(0)=41; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.

Original entry on oeis.org

41, 47, 53, 60, 67, 75, 83, 92, 101, 111, 121, 132, 143, 154, 166, 178, 191, 204, 218, 232, 247, 262, 278, 294, 311, 328, 346, 364, 383, 402, 422, 442, 463, 484, 506, 528, 550, 573, 596, 620, 644, 669, 694, 720, 746, 773, 800, 828, 856, 885, 914, 944, 974, 1005, 1036
Offset: 0

Views

Author

Philippe Deléham, Apr 02 2009

Keywords

Comments

Row 5 in square array A159016.
This sequence contains infinitely many squares. - Philippe Deléham, Apr 04 2009

Crossrefs

Cf. A028392

Programs

  • Mathematica
    NestList[#+Floor[Sqrt[#]]&,41,60] (* Harvey P. Dale, Nov 06 2011 *)

Extensions

More terms from Vincenzo Librandi, Apr 10 2009
Error in sequence corrected by Jon E. Schoenfield, Jun 23 2010
Showing 1-10 of 13 results. Next

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