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 1-4 of 4 results.

A076747 List giving pairs of primes of the form 10k+3 and 10k+13.

Original entry on oeis.org

3, 13, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 223, 233, 283, 293, 373, 383, 433, 443, 643, 653, 673, 683, 733, 743, 853, 863, 1093, 1103, 1153, 1163, 1213, 1223, 1423, 1433, 1483, 1493, 1543, 1553, 1723, 1733, 1993, 2003, 2053, 2063, 2143, 2153
Offset: 1

Views

Author

Cino Hilliard, Nov 12 2002

Keywords

Comments

Except for 3,13, each pair is 30k+13 and 30k+23.

Examples

			163 and 173 are in the sequence because both are prime; 193 and 203 aren't because not both are primes.

Links

Crossrefs

Cf. A076746.

Programs

  • Magma
    &cat[[10*k+3, 10*k+13]: k in [0..250]| IsPrime(10*k+3) and IsPrime(10*k+13)]; // Vincenzo Librandi, Jun 08 2016
  • Mathematica
    Flatten[Select[Table[10 n + {3, 13}, {n, 0, 300}], And@@PrimeQ[#] &]] (* Vincenzo Librandi, Jun 08 2016 *)
  • PARI
    forstep(x=3,2200,10, if(isprime(x) && isprime(x+10), print1(x" "x+10" ")))

Extensions

Edited by Don Reble, Jun 08 2003

A138122 Cousin primes, the lower of which is 7 (mod 10).

Original entry on oeis.org

7, 11, 37, 41, 67, 71, 97, 101, 127, 131, 277, 281, 307, 311, 397, 401, 457, 461, 487, 491, 757, 761, 877, 881, 907, 911, 937, 941, 967, 971, 1087, 1091, 1297, 1301, 1447, 1451, 1567, 1571, 1597, 1601, 1867, 1871, 2137, 2141, 2347, 2351, 2377, 2381, 2437
Offset: 1

Views

Author

Roger L. Bagula, May 04 2008

Keywords

Comments

Start from the intersection of A023200 and A030432, then add the associated members of A046132. The last digits are obviously periodic as A010688. - R. J. Mathar, Nov 26 2008

Links

Crossrefs

Cf. A132243, A132242, A076746.

Programs

  • Mathematica
    a[0] = 7; a[n_] := a[n] = a[n - 1] + 10; Flatten[Table[If[PrimeQ[a[n]] && PrimeQ[a[n] + 4], {a[n],a[n] + 4}, {}], {n, 0, 1000}]]

Extensions

Replaced Mathematica definition by humanly readable phrase. - R. J. Mathar, Nov 26 2008

A162410 Numbers n such that 10*n + 3 and 10*n + 7 are prime.

Original entry on oeis.org

0, 1, 4, 10, 16, 19, 22, 31, 46, 61, 64, 67, 82, 85, 88, 109, 121, 130, 142, 148, 166, 169, 178, 187, 199, 208, 220, 229, 247, 268, 283, 295, 316, 325, 334, 346, 361, 367, 379, 394, 400, 415, 451, 478, 481, 493, 523, 541, 550, 565, 592, 604, 673, 682, 724, 757
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 02 2009

Keywords

Examples

			10*0 + 3 = 3 and 10*0 + 7 = 7 are prime, hence 0 is a term; 10*10 + 3 = 103 and 10*10 + 7 = 107 are prime, hence 10 is a term.

Crossrefs

Cf. A076746.

Programs

  • Magma
    [ n: n in [0..760] | IsPrime(10*n+3) and IsPrime(10*n+7) ]; // Klaus Brockhaus, Jul 07 2009
  • Mathematica
    f1[n_]:=10*n+3; f2[n_]:=10*n+7; lst={};Do[p1=f1[n];p2=f2[n];If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,n]],{n,0,2*6!}];lst
Select[Range[0,1000],And@@PrimeQ[10#+{3,7}]&] (* Harvey P. Dale, May 11 2014 *)

Extensions

Edited and listed terms verified by Klaus Brockhaus, Jul 07 2009

A271367 Primes congruent to 11, 13, 17 or 19 (mod 30).

Original entry on oeis.org

11, 13, 17, 19, 41, 43, 47, 71, 73, 79, 101, 103, 107, 109, 131, 137, 139, 163, 167, 191, 193, 197, 199, 223, 227, 229, 251, 257, 281, 283, 311, 313, 317, 347, 349, 373, 379, 401, 409, 431, 433, 439, 461, 463, 467, 491, 499, 521, 523, 557, 587, 613, 617
Offset: 1

Views

Author

J. M. Bergot, Apr 05 2016

Keywords

Crossrefs

Cf. A000040, A076746.

Programs

  • Magma
    [p: p in PrimesUpTo(700) | p mod 30 in {11,13,17,19}]; // Vincenzo Librandi, Jan 04 2020
  • Maple
    select(isprime, [seq(seq(30*i+k, k = [11,13,17,19]), i=0..100)]); # Robert Israel, Apr 05 2016
  • Mathematica
    Select[Prime[Range[200]],MemberQ[{11,13,17,19},Mod[#,30]]&] (* Harvey P. Dale, Aug 23 2017 *)
  • PARI
    is(n)=n\10%3==1 && isprime(n) \\ Charles R Greathouse IV, Apr 05 2016

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Apr 05 2016
Showing 1-4 of 4 results.

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