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 14 results. Next

A111319 Numbers k such that 5 divides prime(1) + ... + prime(k).

Original entry on oeis.org

2, 3, 9, 11, 17, 25, 29, 31, 51, 53, 57, 62, 71, 77, 85, 89, 91, 101, 103, 105, 116, 118, 131, 147, 153, 156, 159, 167, 173, 180, 186, 188, 190, 195, 209, 226, 230, 239, 242, 245, 256, 259, 261, 266, 268, 283, 292, 298, 303, 314, 317, 324, 349, 352, 357, 364, 366, 368, 376
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111318, A111320, A111321, A111322, A111323, A111324, A111325, A111326, A111327.

Programs

A111320 Numbers k such that 6 divides prime(1) + ... + prime(k).

Original entry on oeis.org

57, 97, 99, 103, 105, 107, 111, 113, 119, 121, 123, 125, 127, 129, 161, 163, 169, 175, 177, 179, 185, 187, 195, 197, 199, 203, 205, 207, 211, 213, 217, 233, 235, 237, 273, 293, 295, 297, 301, 303, 305, 307, 309, 311, 327, 329, 331, 333, 335, 337, 339, 343, 345, 347, 349
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Comments

Odd terms in A103208. - Robert Israel, Jan 26 2019

Links

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111321, A111322, A111323, A111324, A111325, A111326, A111327.

Programs

  • Maple
    P:= [seq(ithprime(i),i=1..1000)]:
L:= ListTools:-PartialSums(P):
select(t -> L[t] mod 6 = 0, [seq(i,i=1..1000)]); # Robert Israel, Jan 26 2019
  • Mathematica
    Position[Accumulate[Prime[Range[400]]], ?(Divisible[#, 6] &)] // Flatten (* _Amiram Eldar, May 14 2024 *)
  • PARI
    lista(pmax) = {my(s = 0, k = 0); forprime(p = 2, pmax, k++; s += p; if(!(s % 6), print1(k, ", ")));} \\ Amiram Eldar, May 14 2024

A111324 Numbers k such that 10 divides prime(1) + ... + prime(k).

Original entry on oeis.org

3, 9, 11, 17, 25, 29, 31, 51, 53, 57, 71, 77, 85, 89, 91, 101, 103, 105, 131, 147, 153, 159, 167, 173, 195, 209, 239, 245, 259, 261, 283, 303, 317, 349, 357, 405, 453, 459, 475, 479, 491, 503, 505, 507, 511, 517, 531, 533, 545, 555, 565, 569, 583, 585, 591, 603, 617, 625
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111323, A111325, A111326, A111327.

Programs

A111318 Numbers k such that 4 divides prime(1) + ... + prime(k).

Original entry on oeis.org

5, 9, 11, 15, 17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 45, 49, 71, 79, 81, 83, 85, 87, 91, 95, 97, 99, 101, 103, 105, 107, 109, 111, 115, 117, 119, 121, 125, 129, 131, 135, 155, 159, 161, 163, 165, 169, 171, 173, 175, 177, 179, 181, 183, 185, 193, 195, 199, 201, 203, 205
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111319, A111320, A111321, A111322, A111323, A111324, A111325, A111326, A111327.

Programs

  • Mathematica
    Module[{nn=300,prs},prs=Accumulate[Prime[Range[nn]]];Select[Range[ nn], Divisible[prs[[#]],4]&]] (* Harvey P. Dale, May 27 2012 *)
  • PARI
    lista(pmax) = {my(s = 0, k = 0); forprime(p = 2, pmax, k++; s += p; if(!(s % 4), print1(k, ", ")));} \\ Amiram Eldar, May 14 2024

A111321 Numbers k such that 7 divides prime(1) + ... + prime(k).

Original entry on oeis.org

5, 8, 13, 22, 33, 40, 47, 50, 56, 63, 72, 84, 86, 104, 106, 110, 115, 126, 128, 139, 148, 150, 154, 157, 160, 180, 184, 186, 188, 200, 209, 220, 228, 230, 232, 236, 238, 240, 244, 253, 270, 274, 300, 302, 305, 322, 324, 331, 339, 354, 367, 371, 384, 415, 417, 420, 428, 433
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111320, A111322, A111323, A111324, A111325, A111326, A111327.

Programs

A111322 Numbers k such that 8 divides prime(1) + ... + prime(k).

Original entry on oeis.org

11, 15, 17, 19, 21, 27, 29, 31, 37, 49, 71, 79, 83, 85, 95, 99, 101, 103, 107, 109, 111, 115, 119, 121, 135, 155, 159, 161, 163, 169, 171, 177, 181, 183, 185, 201, 205, 209, 213, 235, 237, 239, 247, 255, 257, 259, 261, 263, 273, 275, 279, 283, 285, 287, 305, 309, 317, 319
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111323, A111324, A111325, A111326, A111327.

Programs

A111323 Numbers k such that 9 divides prime(1) + ... + prime(k).

Original entry on oeis.org

20, 24, 26, 30, 40, 42, 52, 74, 78, 80, 88, 113, 119, 127, 163, 177, 179, 187, 205, 207, 242, 248, 254, 258, 260, 262, 268, 270, 280, 282, 284, 288, 297, 311, 331, 357, 368, 372, 380, 394, 398, 400, 410, 412, 416, 428, 436, 443, 457, 466, 468, 470, 474, 490, 496, 505, 509
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111324, A111325, A111326, A111327.

Programs

  • Mathematica
    Flatten[Position[Accumulate[Prime[Range[509]]]/9,Integer]] (* _Jayanta Basu, May 18 2013 *)
  • PARI
    lista(pmax) = {my(s = 0, k = 0); forprime(p = 2, pmax, k++; s += p; if(!(s % 9), print1(k, ", ")));} \\ Amiram Eldar, May 14 2024

A111325 Numbers k such that 11 divides prime(1) + ... + prime(k).

Original entry on oeis.org

8, 17, 53, 69, 76, 84, 87, 91, 167, 175, 179, 181, 188, 196, 201, 217, 219, 224, 240, 260, 275, 297, 312, 317, 319, 324, 340, 346, 376, 382, 386, 393, 417, 470, 503, 514, 526, 528, 542, 550, 562, 564, 584, 590, 607, 613, 615, 629, 637, 649, 691, 693, 732, 749, 752, 759
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111323, A111324, A111326, A111327.

Programs

  • Mathematica
    Position[Accumulate[Prime[Range[400]]], ?(Divisible[#, 11] &)] // Flatten (* _Amiram Eldar, May 14 2024 *)
  • PARI
    lista(pmax) = {my(s = 0, k = 0); forprime(p = 2, pmax, k++; s += p; if(!(s % 11), print1(k, ", ")));} \\ Amiram Eldar, May 14 2024
  • Python
    from sympy import nextprime
def aupto(limit):
    p, s, alst = 2, 2, []
    for k in range(1, limit+1):
        if s == 0: alst.append(k)
        p = nextprime(p); s = (s + p)%11
    return alst
print(aupto(759)) # Michael S. Branicky, Aug 17 2021

A111326 Numbers k such that 12 divides prime(1) + ... + prime(k).

Original entry on oeis.org

97, 99, 103, 105, 107, 111, 119, 121, 125, 129, 161, 163, 169, 175, 177, 179, 185, 195, 199, 203, 205, 207, 211, 213, 233, 235, 237, 273, 305, 307, 309, 311, 329, 335, 337, 343, 345, 347, 353, 357, 421, 423, 425, 439, 443, 445, 447, 449, 455, 463, 511, 513, 515, 539
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111323, A111324, A111325, A111327.

Programs

A111327 Numbers k such that 13 divides prime(1) + ... + prime(k).

Original entry on oeis.org

49, 61, 67, 87, 92, 117, 119, 126, 131, 160, 166, 179, 203, 253, 269, 295, 297, 299, 319, 344, 348, 360, 381, 393, 408, 418, 429, 437, 442, 451, 485, 496, 502, 506, 508, 510, 532, 541, 553, 559, 565, 585, 591, 623, 626, 647, 652, 656, 662, 672, 692, 712, 715, 733, 736
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2005

Keywords

Links

Crossrefs

Cf. A007504, A103208, A111318, A111319, A111320, A111321, A111322, A111323, A111324, A111325, A111326.

Programs

Showing 1-10 of 14 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.