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 1-6 of 6 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

A089033 Numbers n such that 7*n+3 is prime.

Original entry on oeis.org

0, 2, 4, 8, 10, 14, 22, 28, 32, 34, 38, 40, 44, 50, 52, 58, 68, 74, 80, 82, 88, 92, 94, 110, 112, 118, 122, 134, 140, 142, 148, 158, 160, 164, 170, 178, 182, 184, 188, 194, 208, 212, 220, 224, 230, 232, 238, 242, 250, 260, 268, 272, 278, 298, 304, 320, 334, 340
Offset: 1

Views

Author

Giovanni Teofilatto, Nov 12 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

A045437 gives primes, A090613 gives prime index.
Cf. A024903, A033868, A090614.

Programs

Formula

a(n) = A024903(n)-1 = A033868(n)-2 = A090614(n)*2.

Extensions

Corrected and extended by Ray Chandler, Nov 12 2003
Offset corrected by Arkadiusz Wesolowski, Aug 09 2011

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.

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

A153347 Numbers n>0 such that 7*n-4 is not prime.

Original entry on oeis.org

2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 34, 36, 37, 38, 40, 42, 43, 44, 46, 47, 48, 49, 50, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92
Offset: 1

Views

Author

Vincenzo Librandi, Dec 24 2008

Keywords

Examples

			Distribution of the odd terms in the following triangular array:
*;
*,*;
*,*,*;
*,7,*,*;
*,*,*,*,*;
*,*,*,*,21,*;
7,*,*,*,*,*,*;
*,*,*,*,*,*,37,*;
*,*,*,25,*,*,*,*,*;
*,*,*,*,*,*,*,*,*,*;
*,17,*,*,*,*,*,*,63,*,*;
*,*,*,*,*,47,*,*,*,*,*,*;
*,*,*,*,43,*,*,*,*,*,*,97,*;
13,*,*,*,*,*,*,71,*,*,*,*,*,*; etc.
where * marks the non-integer values of (4*h*k + 2*k + 2*h + 5)/7 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013

Links

Crossrefs

Cf. A024903.

Programs

  • Magma
    [n: n in [1..150] | not IsPrime(7*n-4)]; // Vincenzo Librandi, Jan 13 2013
  • Mathematica
    Select[Range[1, 200], !PrimeQ[7 # - 4]&] (* Vincenzo Librandi, Jan 13 2013 *)

Extensions

Erroneous comment deleted by N. J. A. Sloane, Jun 23 2010
Showing 1-6 of 6 results.

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

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