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 1-9 of 9 results.

A045437 Primes congruent to 3 mod 7.

Original entry on oeis.org

3, 17, 31, 59, 73, 101, 157, 199, 227, 241, 269, 283, 311, 353, 367, 409, 479, 521, 563, 577, 619, 647, 661, 773, 787, 829, 857, 941, 983, 997, 1039, 1109, 1123, 1151, 1193, 1249, 1277, 1291, 1319, 1361, 1459, 1487, 1543, 1571, 1613, 1627, 1669, 1697, 1753
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Also primes congruent to 3 mod 14.

Links

Crossrefs

Primes arising in sequences A024903, A033868, A089033, A090614.
A090613 gives prime index.

Programs

Extensions

Extended by Ray Chandler, Dec 23 2003

A090614 Numbers n such that 14n+3 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 7, 11, 14, 16, 17, 19, 20, 22, 25, 26, 29, 34, 37, 40, 41, 44, 46, 47, 55, 56, 59, 61, 67, 70, 71, 74, 79, 80, 82, 85, 89, 91, 92, 94, 97, 104, 106, 110, 112, 115, 116, 119, 121, 125, 130, 134, 136, 139, 149, 152, 160, 167, 170, 172, 176, 182, 184, 185
Offset: 1

Views

Author

Ray Chandler, Dec 23 2003

Keywords

Links

Crossrefs

A045437 gives primes, A090613 gives prime index.
Cf. A024903, A033868, A089033.

Programs

Formula

a(n) = (A024903(n+1)-1)/2 = (A033868(n)-2)/2 = A089033(n)/2.

A024903 Numbers k such that 7*k - 4 is prime.

Original entry on oeis.org

1, 3, 5, 9, 11, 15, 23, 29, 33, 35, 39, 41, 45, 51, 53, 59, 69, 75, 81, 83, 89, 93, 95, 111, 113, 119, 123, 135, 141, 143, 149, 159, 161, 165, 171, 179, 183, 185, 189, 195, 209, 213, 221, 225, 231, 233, 239, 243, 251, 261, 269, 273, 279, 299, 305, 321, 335, 341
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A045437 (associated primes), A090613 (gives prime index).
Cf. A033868, A089033, A090614.

Programs

Formula

a(n) = A033868(n-1)-1 = A089033(n-1)+1 = A090614(n-1)*2+1.

A090613 Numbers k such that the k-th prime is congruent to 3 mod 7.

Original entry on oeis.org

2, 7, 11, 17, 21, 26, 37, 46, 49, 53, 57, 61, 64, 71, 73, 80, 92, 98, 103, 106, 114, 118, 121, 137, 138, 145, 148, 160, 166, 168, 175, 186, 188, 190, 196, 204, 206, 210, 215, 218, 232, 236, 243, 248, 255, 258, 263, 265, 273, 281, 289, 292, 296, 316, 321, 334
Offset: 1

Views

Author

Ray Chandler, Dec 23 2003

Keywords

Comments

Also numbers k such that the k-th prime is congruent to 3 mod 14.
A045437 indexed by A000040.
The asymptotic density of this sequence is 1/6 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Crossrefs

Cf. A024903, A033868, A045437, A089033, A090614.

Programs

  • Mathematica
    Select[Range[350], Mod[Prime[#], 7] == 3 &] (* Amiram Eldar, Mar 01 2021 *)

Formula

a(n) = k such that A000040(k) = A045437(n).

Extensions

Offset corrected by Amiram Eldar, Mar 01 2021

A033868 Numbers n such that 7*n-11 is prime.

Original entry on oeis.org

2, 4, 6, 10, 12, 16, 24, 30, 34, 36, 40, 42, 46, 52, 54, 60, 70, 76, 82, 84, 90, 94, 96, 112, 114, 120, 124, 136, 142, 144, 150, 160, 162, 166, 172, 180, 184, 186, 190, 196, 210, 214, 222, 226, 232, 234, 240, 244, 252, 262, 270, 274, 280, 300, 306, 322, 336, 342
Offset: 1

Views

Author

Giovanni Teofilatto, Dec 01 2003

Keywords

References

  • M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.
  • Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta,UTET, CittaStudiEdizioni, Milano 1997.

Links

Crossrefs

Cf. A045437 (associated primes), A090613 (gives prime index).
Cf. A024903, A089033, A090614.

Programs

Formula

a(n) = A024903(n)+1 = A089033(n)+2 = A090614(n)*2+2.

Extensions

Extended by Ray Chandler, Dec 23 2003
Offset corrected by Arkadiusz Wesolowski, Aug 09 2011

A111250 Numbers n such that 7*n + 10 is prime.

Original entry on oeis.org

1, 3, 7, 9, 13, 21, 27, 31, 33, 37, 39, 43, 49, 51, 57, 67, 73, 79, 81, 87, 91, 93, 109, 111, 117, 121, 133, 139, 141, 147, 157, 159, 163, 169, 177, 181, 183, 187, 193, 207, 211, 219, 223, 229, 231, 237, 241, 249, 259, 267, 271, 277, 297, 303, 319, 333, 339, 343
Offset: 1

Views

Author

Parthasarathy Nambi, Oct 31 2005

Keywords

Comments

One less than the entry of A089033 at the same index.

Examples

			If n=117 then 7*n + 10 = 829 (prime).

Links

Crossrefs

Cf. A105772, A024902, A024900.

Programs

  • Magma
    [ n: n in [0..1500] | IsPrime(7*n + 10) ] // Vincenzo Librandi, Jan 31 2011
  • Mathematica
    Select[Range[400],PrimeQ[7#+10]&] (* Harvey P. Dale, Mar 25 2021 *)
  • PARI
    for(n=1,453,if(isprime(7*n + 10),print1(n,",")))

Extensions

Extended by Lambert Klasen (lambert.klasen(AT)gmx.net), Nov 02 2005

A124849 Numbers k such that 7k + 3 and 3k + 7 are primes.

Original entry on oeis.org

0, 2, 4, 8, 10, 22, 32, 34, 40, 44, 50, 52, 58, 68, 74, 88, 92, 110, 122, 134, 142, 160, 164, 178, 188, 208, 212, 242, 250, 260, 268, 272, 304, 320, 334, 344, 352, 370, 374, 382, 388, 398, 424, 428, 440, 458, 464, 472, 484, 494, 508, 520, 524, 538, 550, 554, 572
Offset: 1

Views

Author

Zak Seidov, Nov 10 2006

Keywords

Comments

Intersection of A089033 and A089953.

Links

Crossrefs

Cf. A089033, A089953, A124850.

Programs

  • Magma
    [n: n in [0..1000] | IsPrime(7*n+3) and IsPrime(3*n+7)] // Vincenzo Librandi, Mar 26 2010
  • Mathematica
    Select[Range[0,600],AllTrue[{7#+3,3#+7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 27 2018 *)

A124850 Primes p=n/2 such that 7n+3 and 3n+7 are primes.

Original entry on oeis.org

2, 5, 11, 17, 29, 37, 61, 67, 71, 89, 167, 191, 199, 229, 269, 277, 311, 331, 337, 347, 379, 389, 419, 431, 509, 541, 577, 587, 617, 631, 691, 709, 757, 797, 809, 821, 929, 941, 977, 991, 1069, 1091, 1117, 1129, 1217, 1277, 1279, 1289, 1291, 1367, 1439
Offset: 1

Views

Author

Zak Seidov, Nov 10 2006

Keywords

Links

Crossrefs

Cf. A089033, A089953, A124849.

Programs

  • Mathematica
    Select[Prime[Range[250]],AllTrue[{14#+3,6#+7},PrimeQ]&] (* Harvey P. Dale, Mar 10 2022 *)

A154611 Numbers n such that 7*n+3 is not prime.

Original entry on oeis.org

1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 33, 35, 36, 37, 39, 41, 42, 43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79
Offset: 1

Views

Author

Vincenzo Librandi, Jan 15 2009

Keywords

Comments

The even terms are the integer values of (4*h*k + 2*k + 2*h - 2)/7, where h and k are positive integers. - Vincenzo Librandi, Jan 17 2013
The corresponding composite numbers are 10, 24, 38, 45, 52, 66, 80, 87, 94, 108, 115, 122, 129, ... - Michael B. Porter, Jan 17 2013

Links

Crossrefs

Cf. A089033, A045437, A017017.

Programs

  • Magma
    [n: n in [0..80] | not IsPrime(7*n+3)]; // Vincenzo Librandi, Apr 05 2013
  • Mathematica
    With[{nn=100},Sort[Join[Range[1,nn-1,2],Select[Range[0,nn,2], !PrimeQ[ 7#+3]&]]]] (* Harvey P. Dale, Aug 22 2012 *)
Select[Range[0, 100], !PrimeQ[7 # + 3]&] (* Vincenzo Librandi, Apr 05 2013 *)

Extensions

Erroneous comments deleted by N. J. A. Sloane, Jun 23 2010
Showing 1-9 of 9 results.

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

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