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 22 results. Next

A216292 Values of k such that there is exactly one prime between 10k and 10k + 9.

Original entry on oeis.org

9, 11, 12, 14, 18, 21, 24, 29, 30, 36, 39, 41, 42, 45, 47, 48, 55, 58, 63, 66, 68, 69, 71, 72, 74, 77, 78, 79, 80, 81, 83, 86, 87, 90, 92, 93, 95, 96, 98, 100, 102, 104, 105, 108, 111, 116, 117, 119, 120, 124, 125, 131, 137, 138, 139, 140, 144, 147, 151, 152
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Examples

			36 is in the sequence because between 360 and 369 there is exactly one prime: 367. [_Bruno Berselli_, Sep 04 2012]

Links

Crossrefs

Cf. A007811, A032352, A078494, A216293.

Programs

  • Magma
    [n: n in [1..200] | IsOne(#PrimesInInterval(10*n, 10*n+9))]; // Bruno Berselli, Sep 04 2012
  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[Length[ps] == 1, AppendTo[t, n]], {n, 0, 199}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[200],PrimePi[10#+9]-PrimePi[10#]==1&] (* Harvey P. Dale, Feb 04 2015 *)
  • PARI
    is(n)=isprime(10*n+1)+isprime(10*n+3)+isprime(10*n+7)+isprime(10*n+9)==1 \\ Charles R Greathouse IV, Sep 07 2012
  • Python
    from itertools import count, islice
from sympy import isprime
def A216292_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda k: sum(int(isprime(10*k+i)) for i in (1,3,7,9)) == 1, count(max(1,startvalue)))
A216292_list = list(islice(A216292_gen(),30)) # Chai Wah Wu, Sep 23 2022

Formula

a(n) ~ 0.1 n log n. - Charles R Greathouse IV, Sep 07 2012
a(n) = floor(A078494(n) / 10). - Charles R Greathouse IV, Sep 07 2012

A216293 Values of k such that there are exactly two primes between 10k and 10k + 9.

Original entry on oeis.org

2, 3, 5, 6, 8, 15, 16, 17, 23, 25, 26, 27, 28, 33, 34, 35, 37, 38, 40, 44, 49, 50, 52, 54, 56, 57, 59, 60, 65, 67, 70, 73, 75, 76, 91, 94, 97, 99, 101, 110, 112, 115, 118, 121, 122, 123, 127, 128, 129, 132, 136, 143, 149, 154, 155, 157, 161, 162, 172, 174
Offset: 1

Views

Author

V. Raman, Sep 03 2012

Keywords

Examples

			23 is in the sequence because between 230 and 239 there are exactly two primes: 233 and 239. [_Bruno Berselli_, Sep 04 2012]

Links

Crossrefs

Cf. A032352, A007811, A078494, A216292.

Programs

  • Magma
    [n: n in [1..200] | #PrimesInInterval(10*n, 10*n+9) eq 2]; // Bruno Berselli, Sep 04 2012
  • Mathematica
    t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[Length[ps] == 2, AppendTo[t, n]], {n, 0, 229}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[200],Count[Range[10#,10#+9],?PrimeQ]==2&] (* _Harvey P. Dale, Jan 19 2017 *)

Formula

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

A078500 Primes occurring only twice in a decade.

Original entry on oeis.org

23, 29, 31, 37, 53, 59, 61, 67, 83, 89, 151, 157, 163, 167, 173, 179, 233, 239, 251, 257, 263, 269, 271, 277, 281, 283, 331, 337, 347, 349, 353, 359, 373, 379, 383, 389, 401, 409, 443, 449, 491, 499, 503, 509, 521, 523, 541, 547, 563, 569, 571, 577, 593, 599
Offset: 1

Views

Author

Cino Hilliard, Jan 04 2003

Keywords

Comments

Only 6 such primes will occur in the 21st century.

Links

Crossrefs

Cf. A078494.

Programs

  • Magma
    &cat [PrimesInInterval(10*n+1, 10*n+9): n in [0..50] | #PrimesInInterval(10*n+1, 10*n+9) eq 2]; // Bruno Berselli, Sep 05 2012
  • Mathematica
    Select[Table[Prime[Range[PrimePi[n*10]+1,PrimePi[n*10+10]]],{n,60}],Length[ #] == 2&]//Flatten (* Harvey P. Dale, Aug 09 2020 *)
  • PARI
    decade2pr(n1,n2) = { if(n1==0,n1=10); forstep(x=n1,n2,10, if(isprime(x+1) && isprime(x+3) && !isprime(x+7) && !isprime(x+9), print1(x+1" "x+3" ");); if(isprime(x+1) && isprime(x+7) && !isprime(x+3) && !isprime(x+9), print1(x+1" "x+7" ");); if(isprime(x+1) && isprime(x+9) && !isprime(x+3) && !isprime(x+7), print1(x+1" "x+9" ");); if(isprime(x+3) && isprime(x+7) && !isprime(x+1) && !isprime(x+9), print1(x+3" "x+7" ");); if(isprime(x+3) && isprime(x+9) && !isprime(x+1) && !isprime(x+7), print1(x+3" "x+9" ");); if(isprime(x+7) && isprime(x+9) && !isprime(x+1) && !isprime(x+3), print1(x+7" "x+9" ");); ); }

Extensions

Offset changed to 1 by Alois P. Heinz, Jul 22 2014

A216295 Values of k such that 10k + 1 is the only prime between 10k and 10k + 9.

Original entry on oeis.org

18, 21, 24, 42, 63, 66, 69, 81, 102, 105, 117, 120, 138, 147, 151, 153, 180, 181, 183, 195, 216, 222, 225, 231, 252, 262, 273, 286, 297, 300, 312, 319, 327, 333, 336, 339, 357, 393, 411, 420, 423, 426, 462, 469, 480, 483, 486, 501, 526, 528, 535, 553, 558
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}, AppendTo[t, n]], {n, 0, 669}]; t (* T. D. Noe, Sep 03 2012 *)

Formula

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

A216296 Values of k such that 10k + 3 is the only prime between 10k and 10k + 9.

Original entry on oeis.org

11, 29, 68, 74, 77, 86, 95, 98, 116, 119, 137, 152, 158, 173, 182, 191, 200, 205, 215, 221, 224, 227, 242, 250, 263, 266, 275, 284, 302, 341, 343, 359, 362, 364, 380, 383, 386, 436, 437, 446, 449, 452, 458, 460, 466, 470, 473, 494, 497, 515, 532, 533, 548
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}, AppendTo[t, n]], {n, 0, 647}]; t (* T. D. Noe, Sep 03 2012 *)

Formula

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

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
Showing 1-10 of 22 results. Next

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

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