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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A186407 Numbers k such that there are 15 primes between 100*k and 100*k + 99.

Original entry on oeis.org

8, 12, 16, 22, 23, 26, 33, 40, 49, 63, 75, 94, 375, 424, 1131, 1572, 3442, 3922, 7393, 9780, 13939, 16528, 17492, 29673, 71338, 75877, 237421, 464977, 514483, 687352, 747574, 981953, 1040840, 1269778, 1298137, 1346413, 1790287, 1884223, 2330647, 2527249, 2601874, 2813749
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 12815608 possible prime patterns for centuries having 15 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			8 is in this sequence because there are 15 primes between 800 and 899 (809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883 and 887).

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))==15, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==15, print1((N\100)-1,", ")); s=1; N=100*(p\100+1),s++)) \\ Charles R Greathouse IV, Feb 21 2011

Extensions

a(19)-a(42) from Charles R Greathouse IV, Feb 21 2011

A261571 Number of possible prime patterns for centuries having exactly n primes.

Original entry on oeis.org

1, 40, 780, 7528, 47878, 225044, 830270, 2459376, 5900602, 11555200, 18634704, 24942742, 27836859, 25913910, 20053913, 12815608, 6699888, 2829786, 948729, 245756, 47150, 6276, 518, 20
Offset: 0

Views

Author

Tim Johannes Ohrtmann, Aug 27 2015

Keywords

Comments

The index of the final term is A364678(100) = 23. - Peter Munn, Sep 04 2023

Crossrefs

Cf. A010956.
Cf. A038822 (number of primes between 100n and 100n+99).
Cf. A181098 (centuries without primes).
Cf. A186393-A186408 (centuries having 1 to 16 primes).
Cf. A186509 (centuries having 17 primes).
Cf. A186311 (first occurrences).
Cf. A364678.

A186395 Numbers k such that there are 3 primes between 100*k and 100*k + 99.

Original entry on oeis.org

588, 695, 797, 1430, 1621, 1751, 1809, 1869, 1904, 1913, 2042, 2067, 2123, 2127, 2322, 2471, 2505, 2562, 2734, 2833, 2862, 2874, 2935, 3023, 3077, 3134, 3371, 3380, 3552, 3611, 3679, 3703, 3707, 3725, 3878, 4046, 4167, 4215
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 7528 possible prime patterns for centuries having 3 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			588 is in this sequence because there are 3 primes between 58800 and 58899 (58831, 58889 and 58897).

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))==3, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==3, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

A186396 Numbers k such that there are 4 primes between 100*k and 100*k + 99.

Original entry on oeis.org

314, 356, 524, 662, 831, 881, 1037, 1101, 1124, 1307, 1370, 1433, 1623, 1713, 1733, 1755, 1801, 1808, 1831, 1880, 1956, 2031, 2150, 2178, 2202, 2222, 2231, 2330, 2374, 2502, 2503, 2532, 2545, 2611, 2618, 2656, 2659, 2665
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 47878 possible prime patterns for centuries having 4 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			314 is in this sequence because there are 4 primes between 31400 and 31499 (31469, 31477, 31481 and 31489).

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

A186397 Numbers k such that there are 5 primes between 100*k and 100*k + 99.

Original entry on oeis.org

188, 273, 377, 403, 438, 506, 598, 605, 732, 758, 790, 800, 866, 885, 916, 936, 972, 981, 1031, 1032, 1060, 1074, 1075, 1086, 1103, 1128, 1136, 1193, 1194, 1204, 1218, 1240, 1248, 1265, 1280, 1287, 1293, 1298, 1390, 1400
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

Comments

There are 225044 possible prime patterns for centuries having 5 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			188 is in this sequence because there are 5 primes between 18800 and 18899 (18803, 18839, 18859, 18869 and 18899).

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))==5, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
  • PARI
    N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==5, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

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
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