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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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

A216307 Values of k such that 10*k+3 and 10*k+9 alone are prime between 10*k and 10*k+9.

Original entry on oeis.org

2, 5, 8, 17, 23, 26, 35, 37, 38, 44, 50, 56, 59, 65, 73, 101, 110, 112, 122, 128, 143, 149, 154, 155, 161, 175, 197, 206, 233, 239, 254, 269, 290, 296, 308, 320, 331, 332, 353, 373, 392, 401, 407, 413, 425, 428, 464, 467, 479, 490, 499, 500, 511, 527, 530
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 + 9}, AppendTo[t, n]], {n, 0, 782}]; t (* T. D. Noe, Sep 04 2012 *)
Select[Range[800],Boole[PrimeQ[Range[10 #,10 #+9]]]=={0,0,0,1,0,0,0,0,0,1}&] (* Harvey P. Dale, Apr 23 2019 *)

Formula

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

A216308 Values of k such that 10*k+7 and 10*k+9 are the only primes between 10*k and 10*k+9.

Original entry on oeis.org

34, 127, 202, 223, 226, 265, 352, 355, 412, 433, 454, 463, 496, 619, 694, 730, 838, 853, 859, 967, 976, 1000, 1003, 1042, 1093, 1105, 1171, 1177, 1321, 1339, 1399, 1438, 1444, 1486, 1528, 1741, 1759, 1765, 1774, 1783, 1795, 1828, 1969, 2047, 2050, 2071, 2080
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, 10*n + 9}, AppendTo[t, n]], {n, 0, 2599}]; t (* T. D. Noe, Sep 04 2012 *)

Formula

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

A216309 The prime ending in 1 is the only prime in a decade.

Original entry on oeis.org

181, 211, 241, 421, 631, 661, 691, 811, 1021, 1051, 1171, 1201, 1381, 1471, 1511, 1531, 1801, 1811, 1831, 1951, 2161, 2221, 2251, 2311, 2521, 2621, 2731, 2861, 2971, 3001, 3121, 3191, 3271, 3331, 3361, 3391, 3571, 3931, 4111, 4201, 4231, 4261, 4621, 4691
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Comments

Primes of the form 10n+1 such that 10n+3, 10n+7, and 10n+9 are composite. - Charles R Greathouse IV, Sep 06 2012

Links

Crossrefs

Subsequence of A030430. Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 1}, AppendTo[t, ps[[1]]]], {n, 0, 588}]; t (* T. D. Noe, Sep 04 2012 *)
Select[10*Range[500]+1,PrimeQ[#]&&AllTrue[#+{2,6,8},CompositeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 01 2018 *)

Formula

a(n) ~ 4n log n. - Charles R Greathouse IV, Sep 06 2012

A216310 The prime ending in 3 is the only prime in a decade.

Original entry on oeis.org

113, 293, 683, 743, 773, 863, 953, 983, 1163, 1193, 1373, 1523, 1583, 1733, 1823, 1913, 2003, 2053, 2153, 2213, 2243, 2273, 2423, 2503, 2633, 2663, 2753, 2843, 3023, 3413, 3433, 3593, 3623, 3643, 3803, 3833, 3863, 4363, 4373, 4463, 4493, 4523, 4583, 4603
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Comments

Primes of the form 10n+3 such that 10n+1, 10n+7, and 10n+9 are composite. - Charles R Greathouse IV, Sep 06 2012

Links

Crossrefs

Subsequence of A030431. Cf. A032352, A007811, A078494.

Programs

  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 3}, AppendTo[t, ps[[1]]]], {n, 0, 595}]; t (* T. D. Noe, Sep 04 2012 *)
Select[10*Range[500]+3,PrimeQ[#]&&AllTrue[#+{-2,4,6},CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 27 2016 *)

Formula

a(n) ~ 4n log n. - Charles R Greathouse IV, Sep 06 2012

A216311 The prime ending in 7 is the only prime in a decade.

Original entry on oeis.org

97, 127, 307, 367, 397, 457, 487, 557, 587, 727, 787, 797, 877, 907, 937, 967, 1087, 1117, 1447, 1567, 1597, 1637, 1657, 1777, 1847, 1987, 2437, 2467, 2617, 2647, 2707, 2767, 2777, 2887, 2897, 2917, 2927, 3037, 3137, 3217, 3407, 3457, 3607, 3727, 3847
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Comments

Primes of the form 10n+7 such that 10n+1, 10n+3, and 10n+9 are composite. - Charles R Greathouse IV, Sep 06 2012

Links

Crossrefs

Subsequence of A030432.
Cf. A032352, A007811, A078494.

Programs

  • Magma
    [p: p in PrimesUpTo(4000) | p mod 10 eq 7 and IsOne(#PrimesInInterval(10*t+1, 10*t+9)) where t is Floor(p/10)]; // Bruno Berselli, Sep 14 2012
  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 7}, AppendTo[t, ps[[1]]]], {n, 0, 529}]; t (* T. D. Noe, Sep 04 2012 *)

Formula

a(n) ~ 4n log n. - Charles R Greathouse IV, Sep 06 2012
Previous Showing 11-20 of 22 results. Next

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