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.

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A186398 Numbers k such that there are 6 primes between 100*k and 100*k + 99.

Original entry on oeis.org

186, 234, 319, 332, 340, 380, 384, 443, 444, 450, 469, 489, 542, 548, 554, 574, 611, 632, 645, 681, 683, 696, 716, 725, 731, 746, 749, 754, 805, 814, 829, 859, 873, 897, 907, 956, 963, 966, 977, 1000, 1008, 1027, 1044, 1050
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 830270 possible prime patterns for centuries having 6 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			186 is in this sequence because there are 6 primes between 18600 and 18699 (18617, 18637, 18661, 18671, 18679 and 18691).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • Mathematica
    Select[Range[1100],PrimePi[100#+99]-PrimePi[100#]==6&] (* Harvey P. Dale, Jun 24 2018 *)
  • PARI
    for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==6, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==6, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186399 Numbers k such that there are 7 primes between 100*k and 100*k + 99.

Original entry on oeis.org

59, 95, 142, 165, 167, 191, 196, 206, 212, 242, 252, 281, 283, 297, 299, 318, 349, 357, 372, 385, 394, 406, 407, 414, 417, 425, 431, 433, 452, 457, 459, 462, 470, 480, 482, 504, 510, 533, 551, 555, 563, 585, 595, 599, 604
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 2459376 possible prime patterns for centuries having 7 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			59 is in this sequence because there are 7 primes between 5900 and 5999 (5903, 5923, 5927, 5939, 5953, 5981 and 5987).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • Mathematica
    Select[Range[610],PrimePi[100#+99]-PrimePi[100#]==7&] (* Harvey P. Dale, Nov 05 2011 *)
  • PARI
    for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==7, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==7, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186400 Numbers k such that there are 8 primes between 100*k and 100*k + 99.

Original entry on oeis.org

48, 64, 84, 105, 116, 135, 141, 149, 155, 162, 176, 178, 189, 204, 219, 224, 228, 231, 243, 245, 247, 248, 250, 255, 258, 260, 265, 271, 275, 289, 296, 307, 309, 328, 339, 361, 371, 374, 390, 396, 399, 402, 409, 413, 428, 432
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 5900602 possible prime patterns for centuries having 8 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			48 is in this sequence because there are 8 primes between 4800 and 4899 (4801, 4813, 4817, 4831, 4861, 4871, 4877 and 4889).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • PARI
    for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==8, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==8, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186401 Numbers k such that there are 9 primes between 100*k and 100*k + 99.

Original entry on oeis.org

41, 43, 70, 73, 83, 89, 99, 115, 117, 120, 123, 128, 132, 138, 143, 150, 158, 161, 163, 168, 171, 172, 193, 200, 202, 208, 209, 216, 222, 223, 225, 229, 233, 237, 239, 246, 276, 278, 282, 288, 290, 294, 300, 302, 303, 304
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 11555200 possible prime patterns for centuries having 9 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			41 is in this sequence because there are 9 primes between 4100 and 4199 (4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159 and 4177).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • Mathematica
    Select[Range[350],PrimePi[100#+99]-PrimePi[100#]==9&] (* Harvey P. Dale, Sep 05 2023 *)
  • PARI
    for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==9, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==9, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186402 Numbers k such that there are 10 primes between 100*k and 100*k + 99.

Original entry on oeis.org

21, 24, 31, 52, 53, 57, 66, 71, 77, 78, 79, 81, 102, 104, 108, 109, 110, 112, 113, 127, 133, 140, 146, 159, 175, 177, 180, 185, 197, 198, 205, 214, 232, 244, 254, 257, 263, 264, 266, 269, 270, 272, 274, 287, 292, 295, 298
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 18634704 possible prime patterns for centuries having 10 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			21 is in this sequence because there are 10 primes between 2100 and 2199 (2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161 and 2179).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • Mathematica
    Select[Range[300], PrimePi[100 # + 99] - PrimePi[100 #]==10 &] (* Vincenzo Librandi, Feb 13 2015 *)
  • PARI
    for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==10, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==10, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186403 Numbers k such that there are 11 primes between 100*k and 100*k + 99.

Original entry on oeis.org

13, 25, 29, 32, 34, 38, 39, 44, 51, 61, 65, 72, 74, 80, 87, 90, 92, 93, 97, 100, 107, 111, 114, 121, 130, 134, 139, 154, 170, 181, 182, 183, 184, 187, 190, 192, 195, 210, 213, 217, 218, 227, 249, 251, 261, 262, 267, 279, 280
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 24942742 possible prime patterns for centuries having 11 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			13 is in this sequence because there are 11 primes between 1300 and 1399 (1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381 and 1399).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • Mathematica
    Select[Range[300],PrimePi[100#+99]-PrimePi[100#]==11&] (* Harvey P. Dale, Jul 26 2011 *)
  • PARI
    for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==11, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==11, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186404 Numbers k such that there are 12 primes between 100*k and 100*k + 99.

Original entry on oeis.org

11, 15, 17, 18, 28, 30, 37, 45, 46, 47, 50, 56, 60, 67, 68, 76, 85, 91, 98, 101, 103, 106, 118, 122, 125, 126, 129, 131, 136, 137, 144, 145, 148, 151, 152, 153, 157, 160, 164, 169, 173, 199, 203, 207, 221, 226, 235, 236, 241
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 27836859 possible prime patterns for centuries having 12 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			11 is in this sequence because there are 12 primes between 1100 and 1199 (1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187 and 1193).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • Mathematica
    Select[Range[250],PrimePi[100#+99]-PrimePi[100#]==12&] (* Harvey P. Dale, Sep 20 2011 *)
  • PARI
    for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==12, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==12, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186405 Numbers k such that there are 13 primes between 100*k and 100*k + 99.

Original entry on oeis.org

19, 36, 54, 55, 62, 69, 86, 88, 96, 119, 124, 156, 166, 174, 201, 211, 215, 220, 238, 240, 308, 320, 323, 329, 355, 408, 412, 416, 427, 442, 544, 569, 606, 616, 633, 636, 674, 713, 775, 798, 806, 832, 875, 888, 900, 923, 1098
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 25913910 possible prime patterns for centuries having 13 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			19 is in this sequence because there are 13 primes between 1900 and 1999 (1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997 and 1999).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • PARI
    for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==13, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==13, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186406 Numbers k such that there are 14 primes between 100*k and 100*k + 99.

Original entry on oeis.org

5, 7, 9, 20, 27, 35, 82, 147, 179, 277, 286, 514, 556, 694, 709, 796, 810, 1158, 1363, 1416, 2033, 2173, 2232, 2297, 2660, 3054, 3274, 4508, 4996, 6635, 8194, 8237, 11047, 11467, 12303, 16166, 19543, 19882, 19936
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 20053913 possible prime patterns for centuries having 14 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			5 is in this sequence because there are 14 primes between 500 and 599 (503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593 and 599).

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • Mathematica
    Select[Range[20000],PrimePi[100#+99]-PrimePi[100#]==14&] (* Harvey P. Dale, Jun 20 2021 *)
  • PARI
    for(n=1, 1e6, if(sum(k=100*n,100*(n+1), ispseudoprime(k))==14, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==14, print1((N\100)-1,", ")); s=1; N=100*(p\100+1),s++)) \\ Charles R Greathouse IV, Feb 21 2011

Extensions

a(30)-a(39) from Charles R Greathouse IV, Feb 21 2011

A276355 Sum of primes between 100*n and 100*n + 99.

Original entry on oeis.org

1060, 3167, 4048, 5612, 7649, 7760, 10316, 10466, 12719, 13330, 16826, 13780, 18775, 14759, 24773, 18666, 24679, 21022, 22230, 25413, 28750, 21398, 33781, 35381, 24452, 28057, 39905, 38474, 34168, 32407, 36560, 31544, 35669, 50157, 38009, 49688, 47439, 44994
Offset: 0

Views

Author

Bhushan Bade, Aug 31 2016

Keywords

Comments

The first occurrence of 0 in this sequence is as a(16718). - Robert Israel, Dec 28 2022

Examples

			Sum of primes in first interval of one hundred numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 is equal to first term i.e 1060.

Links

Crossrefs

Cf. A034387, A038822, A181098.

Programs

  • Maple
    R:= NULL: m:= 0: p:= 0: s:= 0:
while m <= 100 do
  p:= nextprime(p);
  r:= floor(p/100);
  if r = m then
    s:= s + p;
  else
    R:= R, s;
    if m < r-1 then R:= R, 0$(r-1-m) fi;
    s:= p;
    m:= r;
  fi
od:
R;
  • Mathematica
    Table[Total@ Select[Range[#, # + 99] &[100 n], PrimeQ], {n, 0, 37}] (* Michael De Vlieger, Sep 01 2016 *)

Formula

a(n) = A034387(100*(n+1)) - A034387(100*n). - Robert Israel, Aug 31 2016

Extensions

Definition by Omar E. Pol, Aug 31 2016
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