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 10 results.

A181098 Primefree centuries (i.e., numbers k such that no prime exists between 100*k and 100*k+99).

Original entry on oeis.org

16718, 26378, 31173, 39336, 46406, 46524, 51782, 55187, 58374, 58452, 60129, 60850, 63338, 63762, 67898, 69587, 71299, 75652, 78035, 78269, 80277, 83674, 84213, 89052, 95490, 97080, 100881, 101527, 103438, 105916, 111772, 112967
Offset: 1

Views

Author

Jeff Burch, Oct 02 2010

Keywords

Comments

The first consecutive terms are 473267, 473268; see A190639. - M. F. Hasler, May 15 2011

Examples

			16718 is a term because there is no prime between 1671800 and 1671899.

Links

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
Cf. A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

  • Mathematica
    Flatten[Position[Differences[PrimePi[100*Range[0,113000]]],0]]-1 (* Harvey P. Dale, Dec 18 2021 *)
  • PARI
    is(n)=nextprime(100*n)>100*n+99 \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = n + 100n/log n - O(n/log^2 n). - Charles R Greathouse IV, Sep 08 2017

A219996 Centuries whose prime pattern is the same as prime pattern in the previous century.

Original entry on oeis.org

473268, 726761, 1773440, 1808829, 1919129, 2131584, 2165421, 2339972, 2390653, 2518489, 2802592, 2844915, 2982585, 2996185, 3183264, 3193176, 3250987, 3418186, 3428242, 3633473, 3909325, 3953450, 4280456, 4303820, 4373400, 4658286, 4728654, 4978361, 5165403, 5254366
Offset: 1

Views

Author

V. Raman, Dec 08 2012

Keywords

Comments

x belongs to this sequence if and only if the primality character of (100 * (x-1)) + k is the same as (100 * x) + k for all k = 0..99.

Crossrefs

Cf. A181098.
Cf. A190639 (lower century).

Formula

a(n) ~ n. In particular there are x - 200x/log x + O(x/log^2 x) members of this sequence below x. - Charles R Greathouse IV, Dec 09 2012
a(n) = A190639(n) + 1.

A216287 Decades whose prime pattern repeat in the next decade.

Original entry on oeis.org

37, 78, 113, 124, 133, 134, 139, 154, 167, 180, 218, 234, 248, 276, 288, 291, 310, 314, 323, 331, 347, 374, 418, 430, 436, 444, 476, 484, 499, 512, 524, 532, 536, 545, 558, 560, 575, 596, 609, 616, 624, 640, 648, 650, 674, 692, 696, 706, 708, 713, 717, 726
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A190639.
Cf. A219999 (upper decade).

Programs

  • Mathematica
    ps0 = {2, 3, 5, 7}; t = {}; Do[ps1 = Select[Range[10 n, 10 n + 9], PrimeQ]; If[Length[ps0] == Length[ps1] && ps0 + 10 == ps1, AppendTo[t, n - 1]];  ps0 = ps1, {n, 2, 1000}]; t (* T. D. Noe, Sep 03 2012 *)
  • PARI
    isok(i)=isprime(10*i+1)==isprime(10*i+11) && isprime(10*i+3)==isprime(10*i+13) && isprime(10*i+7)==isprime(10*i+17) && isprime(10*i+9)==isprime(10*i+19) \\ V. Raman, Dec 08 2012

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 07 2012
a(n) = A219999(n) - 1. - V. Raman, Dec 08 2012

A216288 Prime-free decades such that the next decade is also prime-free.

Original entry on oeis.org

113, 133, 134, 167, 218, 248, 314, 323, 347, 374, 418, 430, 476, 484, 512, 524, 536, 545, 560, 575, 596, 640, 650, 674, 692, 708, 713, 726, 737, 776, 797, 833, 839, 847, 848, 890, 907, 935, 944, 956, 998, 1001, 1004, 1037, 1040, 1080, 1081, 1091, 1133, 1175
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Comments

Numbers n such that 10n+1, 10n+3, 10n+7, 10n+9, 10n+11, 10n+13, 10n+17, and 10n+19 are composite. - Charles R Greathouse IV, Sep 07 2012

Links

Crossrefs

Cf. A190639, A032352.
Cf. A219998 (upper decade).

Programs

  • Magma
    /* After the Greathouse's comment: */ [n: n in [0..1200] | forall{10*n+i: i in [1,3,7,9,11,13,17,19] | not IsPrime(10*n+i)}]; // Bruno Berselli, Sep 14 2012
  • Mathematica
    ps0 = {2, 3, 5, 7}; t = {}; Do[ps1 = Select[Range[10*n, 10*n + 9], PrimeQ]; If[Length[ps0] == Length[ps1] == 0, AppendTo[t, n-1]]; ps0 = ps1, {n, 2, 1000}]; t (* T. D. Noe, Sep 03 2012 *)
  • PARI
    is(n)=nextprime(10*n)-10*n>20 \\ Charles R Greathouse IV, Sep 07 2012
  • PARI
    is(n)=!(isprime(10*n+1) || isprime(10*n+3) || isprime(10*n+7) || isprime(10*n+9) || isprime(10*n+11) || isprime(10*n+13) || isprime(10*n+17) || isprime(10*n+19)) \\ Charles R Greathouse IV, Sep 07 2012
  • PARI
    for(i=2, 1200, if(isprime(10*i+1)==0&&isprime(10*i+3)==0&&isprime(10*i+7)==0&&isprime(10*i+9)==0&&isprime(10*i+11)==0&&isprime(10*i+13)==0&&isprime(10*i+17)==0&&isprime(10*i+19)==0, print1(i", "))) /* V. Raman, Dec 08 2012 */

Formula

a(n) ~ n. - Charles R Greathouse IV, Sep 07 2012
a(n) = A219998(n) - 1. - V. Raman, Dec 08 2012

A216329 Decades whose prime pattern is the same as the prime pattern in the next decade, with at least one prime.

Original entry on oeis.org

37, 78, 124, 139, 154, 180, 234, 276, 288, 291, 310, 331, 436, 444, 499, 532, 558, 609, 616, 624, 648, 696, 706, 717, 750, 820, 856, 873, 894, 951, 961, 973, 1047, 1072, 1099, 1114, 1188, 1270, 1309, 1347, 1351, 1356, 1366, 1383, 1414, 1419, 1429, 1447, 1473
Offset: 1

Views

Author

V. Raman, Sep 04 2012

Keywords

Links

Crossrefs

Cf. A190639.
Cf. A219997 (upper decade).

Programs

  • Mathematica
    ps0 = {2, 3, 5, 7}; n = 0; t = {}; While[Length[t] < 50, n++; ps1 = Select[Range[10 n, 10 n + 9], PrimeQ]; If[Length[ps0] > 0 && Length[ps0] == Length[ps1] && ps0 + 10 == ps1, AppendTo[t, n - 1]]; ps0 = ps1]; t (* T. D. Noe, Sep 04 2012 *)
  • PARI
    isok(i) = { isprime(10*i+1)==isprime(10*i+11) && isprime(10*i+3)==isprime(10*i+13) && isprime(10*i+7)==isprime(10*i+17) && isprime(10*i+9)==isprime(10*i+19) && isprime(10*i+1)+isprime(10*i+3)+isprime(10*i+7)+isprime(10*i+9)>=1 } \\ V. Raman, Dec 08 2012

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 06 2012
a(n) = A219997(n) - 1. - V. Raman, Dec 08 2012

A219997 Decades whose prime pattern is same as the prime pattern in the previous decade, with at least one prime.

Original entry on oeis.org

38, 79, 125, 140, 155, 181, 235, 277, 289, 292, 311, 332, 437, 445, 500, 533, 559, 610, 617, 625, 649, 697, 707, 718, 751, 821, 857, 874, 895, 952, 962, 974, 1048, 1073, 1100, 1115, 1189, 1271, 1310, 1348, 1352, 1357, 1367, 1384, 1415, 1420, 1430, 1448, 1474
Offset: 1

Views

Author

V. Raman, Dec 07 2012

Keywords

Links

Crossrefs

Cf. A190639.
Cf. A216329 (lower decade).

Programs

  • PARI
    for(i=2, 1500, if(isprime(10*i-9)==isprime(10*i+1)&&isprime(10*i-7)==isprime(10*i+3)&&isprime(10*i-3)==isprime(10*i+7)&&isprime(10*i-1)==isprime(10*i+9)&&isprime(10*i+1)+isprime(10*i+3)+isprime(10*i+7)+isprime(10*i+9)>=1, print1(i", ")))

Formula

a(n) >> n log^2 n.
a(n) = A216329(n) + 1.

A219998 Prime-free decades such that the previous decade is also prime-free.

Original entry on oeis.org

114, 134, 135, 168, 219, 249, 315, 324, 348, 375, 419, 431, 477, 485, 513, 525, 537, 546, 561, 576, 597, 641, 651, 675, 693, 709, 714, 727, 738, 777, 798, 834, 840, 848, 849, 891, 908, 936, 945, 957, 999, 1002, 1005, 1038, 1041, 1081, 1082, 1092, 1134, 1176
Offset: 1

Views

Author

V. Raman, Dec 07 2012

Keywords

Comments

Numbers n such that 10n-9, 10n-7, 10n-3, 10n-1, 10n+1, 10n+3, 10n+7, and 10n+9 are composite.

Links

Crossrefs

Cf. A190639, A032352.
Cf. A216288 (lower decade).

Programs

  • PARI
    for(i=2, 1200, if(isprime(10*i-9)==0&&isprime(10*i-7)==0&&isprime(10*i-3)==0&&isprime(10*i-1)==0&&isprime(10*i+1)==0&&isprime(10*i+3)==0&&isprime(10*i+7)==0&&isprime(10*i+9)==0, print1(i", ")))

Formula

a(n) ~ n.
a(n) = A216288(n) + 1.

A219999 Decades whose prime pattern is the same as prime pattern in the previous decade.

Original entry on oeis.org

38, 79, 114, 125, 134, 135, 140, 155, 168, 181, 219, 235, 249, 277, 289, 292, 311, 315, 324, 332, 348, 375, 419, 431, 437, 445, 477, 485, 500, 513, 525, 533, 537, 546, 559, 561, 576, 597, 610, 617, 625, 641, 649, 651, 675, 693, 697, 707, 709, 714, 718, 727
Offset: 1

Views

Author

V. Raman, Dec 07 2012

Keywords

Examples

			The primes between 380 and 390 are 383 and 389. The primes in the previous decade are 373 and 379. Therefore 38 is in the sequence.

Links

Crossrefs

Cf. A190639.
Cf. A216287 (lower decade).

Programs

  • Mathematica
    Select[Range[2, 1000], Mod[Prime[Range[PrimePi[NextPrime[10#]], PrimePi[10# + 10]]], 10] == Mod[Prime[Range[PrimePi[NextPrime[10# - 10]], PrimePi[10#]]], 10] &] (* Alonso del Arte, Dec 07 2012 *)
  • PARI
    for(i=2, 1000, if( isprime(10*i-9)==isprime(10*i+1) && isprime(10*i-7)==isprime(10*i+3) && isprime(10*i-3)==isprime(10*i+7) && isprime(10*i-1)==isprime(10*i+9), print1(i", ")))

Formula

a(n) >> n log^2 n.
a(n) = A216287(n) + 1.

A228271 Prime-free centuries such that the next century is also prime-free.

Original entry on oeis.org

473267, 1919128, 2131583, 2390652, 2844914, 2982584, 3909324, 4280455, 4658285, 4728653, 5165402, 5254365, 5369468, 5458298, 5551421, 5647232, 5817553, 6070101, 6334188, 6495802, 6877047, 7027013, 7074295, 7087303, 7157062, 7369010, 7392411, 7946633, 8469597
Offset: 1

Views

Author

Arkadiusz Wesolowski, Aug 19 2013

Keywords

Examples

			473267 is in the sequence because there is no prime between 47326699 and 47326900.

Links

Crossrefs

Cf. A181098, A190639.

Programs

  • PARI
    d=100; for(n=1, 10^7, if(nextprime(d*n)>d*(n+2), print1(n, ", ")));

A258275 a(n) = smallest number k > n such that the interval k*100 to k*100+99 has exactly the same prime pattern as the interval n*100 to n*100+99 (or 0 if no such term is known).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4812895043702, 0, 38905562023, 0, 2406071834559, 0, 834998571515, 15367548589719, 274894696197322, 0, 3339850458, 0, 0, 90345210525, 127636130731, 0, 0, 7916673590887, 498009080381, 1128063679395, 616923037, 301998772331
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Jun 25 2015

Keywords

Examples

			a(13) = 38905562023 because the primes between 1300 and 1399 are 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381 and 1399 and 38905562023 is the least century>13 that has exactly the same prime pattern: 3890556202301, 3890556202303, 3890556202307, 3890556202319, 3890556202321, 3890556202327, 3890556202361, 3890556202367, 3890556202373, 3890556202381, 3890556202399.

Crossrefs

Cf. A164987, A190639, A219996.
Showing 1-10 of 10 results.

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

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