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.

Previous Showing 21-30 of 53 results. Next

A216297 Values of k such that 10k + 7 is the only prime between 10k and 10k + 9.

Original entry on oeis.org

9, 12, 30, 36, 39, 45, 48, 55, 58, 72, 78, 79, 87, 90, 93, 96, 108, 111, 144, 156, 159, 163, 165, 177, 184, 198, 243, 246, 261, 264, 270, 276, 277, 288, 289, 291, 292, 303, 313, 321, 340, 345, 360, 372, 384, 387, 390, 396, 417, 429, 432, 435, 450, 498, 507
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 7}, AppendTo[t, n]], {n, 0, 639}]; t (* T. D. Noe, Sep 03 2012 *)

Formula

a(n) ~ 0.4 n log n. - Charles R Greathouse IV, Sep 07 2012

A216298 Values of k such that 10k + 9 is the only prime between 10k and 10k + 9.

Original entry on oeis.org

14, 41, 47, 71, 80, 83, 92, 100, 104, 124, 125, 131, 139, 140, 170, 188, 194, 203, 209, 212, 217, 230, 245, 257, 260, 272, 278, 281, 287, 293, 299, 307, 310, 311, 329, 335, 338, 344, 365, 371, 377, 398, 404, 422, 434, 440, 488, 491, 503, 509, 518, 520, 551
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 9}, AppendTo[t, n]], {n, 0, 677}]; t (* T. D. Noe, Sep 03 2012 *)

Formula

a(n) ~ 0.4 n log n. - Charles R Greathouse IV, Sep 07 2012

A216299 Numbers k such that 10k+1 is composite but 10k+3, 10k+7, 10k+9 are all prime.

Original entry on oeis.org

22, 61, 85, 142, 166, 169, 178, 199, 268, 316, 415, 451, 478, 541, 682, 775, 787, 862, 1045, 1111, 1237, 1387, 1618, 1720, 1738, 2014, 2035, 2074, 2131, 2215, 2305, 2362, 2410, 2710, 2773, 2938, 3013, 3055, 3271, 3334, 3361, 3412, 3652, 4012, 4042, 4069
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Magma
    [k:k in [1..4100]| not IsPrime(10*k+1) and forall{m:m in [3,7,9]| IsPrime(10*k+m)}]; // Marius A. Burtea, Feb 02 2020
  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 3, 10*n + 7, 10*n + 9}, AppendTo[t, n]], {n, 0, 4978}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[4100],CompositeQ[10#+1]&&AllTrue[10#+{3,7,9},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 14 2019 *)

Formula

a(n) >> n log^3 n. - Charles R Greathouse IV, Sep 07 2012

A216300 Numbers k such that 10k+3 is composite but 10k+1, 10k+7, 10k+9 are all prime.

Original entry on oeis.org

13, 160, 376, 391, 421, 547, 586, 712, 745, 748, 754, 808, 883, 985, 1006, 1210, 1291, 1333, 1375, 1462, 1513, 1588, 1702, 1798, 2203, 2269, 2302, 2353, 2497, 2584, 2854, 2920, 3205, 3358, 3436, 3583, 3823, 3832, 3856, 3982, 4003, 4084, 4138, 4339, 4402
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 1, 10*n + 7, 10*n + 9}, AppendTo[t, n]], {n, 0, 4738}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[5000],Boole[PrimeQ[10 #+{1,3,7,9}]]=={1,0,1,1}&] (* Harvey P. Dale, Jan 29 2025 *)

Formula

a(n) >> n log^3 n. - Charles R Greathouse IV, Sep 07 2012

A216301 Numbers k such that 10k+7 is composite but 10k+1, 10k+3, 10k+9 are all prime.

Original entry on oeis.org

7, 43, 103, 106, 145, 238, 271, 409, 472, 544, 574, 670, 721, 904, 934, 1009, 1183, 1204, 1261, 1282, 1372, 1636, 1669, 1729, 1792, 1921, 1975, 2002, 2149, 2152, 2254, 2320, 2437, 2560, 2593, 2611, 2695, 2779, 2857, 2866, 2875, 3085, 3115, 3118, 3256
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 1, 10*n + 3, 10*n + 9}, AppendTo[t, n]], {n, 0, 4999}]; t (* T. D. Noe, Sep 03 2012 *)
cprQ[n_]:=Module[{c=10n},!PrimeQ[c+7]&&And@@PrimeQ[c+{1,3,9}]]; Select[ Range[ 4000],cprQ] (* Harvey P. Dale, May 28 2014 *)
Select[Range[4000],Boole[PrimeQ[10 #+{1,3,7,9}]]=={1,1,0,1}&] (* Harvey P. Dale, Dec 09 2022 *)

Formula

a(n) >> n log^3 n. - Charles R Greathouse IV, Sep 07 2012

A216302 Numbers k such that 10k+9 is composite but 10k+1, 10k+3, 10k+7 are all prime.

Original entry on oeis.org

4, 31, 46, 64, 88, 109, 130, 367, 400, 493, 523, 550, 823, 829, 886, 946, 1033, 1117, 1369, 1390, 1408, 1432, 1825, 1999, 2161, 2329, 2356, 2374, 2503, 2626, 2668, 2671, 2794, 2902, 3049, 3139, 3151, 3154, 3232, 3253, 3421, 3553, 3559, 3601, 3799, 3904
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 1, 10*n + 3, 10*n + 7}, AppendTo[t, n]], {n, 0, 4903}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[4000],!PrimeQ[10#+9]&&And@@PrimeQ[10#+{1,3,7}]&] (* Harvey P. Dale, May 23 2014 *)
Select[Range[4000],Boole[PrimeQ[10 #+{1,3,7,9}]]=={1,1,1,0}&] (* Harvey P. Dale, Feb 14 2025 *)

Formula

a(n) >> n log^3 n. - Charles R Greathouse IV, Sep 07 2012

A216303 Numbers k such that 10k+1 and 10k+3 are prime but 10k+7 and 10k+9 are composite.

Original entry on oeis.org

28, 52, 115, 172, 193, 211, 214, 259, 280, 337, 358, 382, 385, 424, 427, 442, 448, 502, 613, 655, 676, 679, 733, 901, 928, 1027, 1030, 1135, 1207, 1216, 1225, 1393, 1456, 1459, 1558, 1597, 1645, 1663, 1690, 1768, 1813, 1831, 1852, 1918, 1954, 1984, 1996, 2023
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Examples

			28 is a member since 281 & 283 are prime while 287 & 289 are composite.

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 1, 10*n + 3}, AppendTo[t, n]], {n, 0, 2689}]; t (* T. D. Noe, Sep 04 2012 *)
Select[Range[2100],PrimeQ[10#+{1,3,7,9}]=={True,True,False,False}&] (* Harvey P. Dale, Dec 17 2014 *)

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 07 2012

Extensions

Definition corrected by Harvey P. Dale, Dec 17 2014

A216304 Values of k such that 10*k+1 and 10*k+7 alone are prime between 10*k and 10*k+9.

Original entry on oeis.org

3, 6, 15, 25, 27, 33, 54, 57, 60, 75, 94, 97, 99, 118, 123, 129, 132, 136, 162, 174, 186, 190, 201, 213, 228, 234, 235, 237, 241, 244, 255, 267, 279, 285, 306, 318, 330, 351, 354, 363, 369, 402, 405, 439, 444, 445, 456, 459, 465, 487, 495, 508, 510, 538
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 1, 10*n + 7}, AppendTo[t, n]], {n, 0, 699}]; t (* T. D. Noe, Sep 04 2012 *)
Select[Range[600],Boole[PrimeQ[Range[10 #,10 #+9]]]=={0,1,0,0,0,0,0,1,0,0}&] (* Harvey P. Dale, Sep 15 2016 *)

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 07 2012

A216305 Values of k such that 10*k+1 and 10*k+9 alone are prime between 10*k and 10*k+9.

Original entry on oeis.org

40, 49, 70, 76, 91, 157, 253, 274, 301, 304, 322, 349, 370, 388, 475, 505, 517, 622, 652, 715, 769, 817, 868, 931, 994, 1015, 1039, 1063, 1078, 1132, 1168, 1228, 1240, 1279, 1315, 1324, 1378, 1441, 1477, 1555, 1567, 1687, 1723, 1735, 1819, 1837, 1867, 1900
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 1, 10*n + 9}, AppendTo[t, n]], {n, 0, 3319}]; t (* T. D. Noe, Sep 04 2012 *)

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 07 2012

A216306 Values of k such that 10*k+3 and 10*k+7 alone are prime between 10*k and 10*k+9.

Original entry on oeis.org

16, 67, 121, 220, 229, 247, 283, 295, 334, 361, 379, 394, 481, 592, 604, 673, 724, 757, 760, 772, 793, 844, 880, 913, 988, 1024, 1066, 1108, 1144, 1159, 1186, 1192, 1234, 1243, 1303, 1318, 1396, 1417, 1453, 1465, 1471, 1501, 1507, 1537, 1549, 1660, 1762, 1858
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Links

Crossrefs

Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 3, 10*n + 7}, AppendTo[t, n]], {n, 0, 2476}]; t (* T. D. Noe, Sep 04 2012 *)
Select[Range[2000],Boole[PrimeQ[10#+{1,3,7,9}]]=={0,1,1,0}&] (* Harvey P. Dale, Jul 20 2021 *)

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 07 2012
Previous Showing 21-30 of 53 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.