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.

A172367 Numbers k > 0 such that k+4 is a prime.

Original entry on oeis.org

1, 3, 7, 9, 13, 15, 19, 25, 27, 33, 37, 39, 43, 49, 55, 57, 63, 67, 69, 75, 79, 85, 93, 97, 99, 103, 105, 109, 123, 127, 133, 135, 145, 147, 153, 159, 163, 169, 175, 177, 187, 189, 193, 195, 207, 219, 223, 225, 229, 235, 237, 247, 253, 259, 265, 267, 273, 277, 279
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 01 2010

Keywords

Comments

The subsequence of primes A023200 consists of the smallest primes p of cousin prime pairs (p, p+4), while the subsequence of nonprimes is A164384. - Bernard Schott, Oct 19 2021

Examples

			a(1) = 5 - 4 = 1, a(2) = 7 - 4 = 3.

Links

Crossrefs

Union of A023200 and A164384.
Cf. A000040, A006093, A040976, A086801.

Programs

Formula

a(n) = prime(n+2) - 4.

A164385 Composite numbers n such that n+4 and n-4 are both prime.

Original entry on oeis.org

9, 15, 27, 33, 57, 63, 75, 93, 105, 135, 153, 177, 195, 237, 267, 273, 363, 393, 405, 435, 453, 483, 495, 567, 573, 597, 603, 657, 687, 705, 723, 747, 765, 825, 915, 933, 987, 1017, 1035, 1065, 1113, 1167, 1197, 1227, 1233, 1287, 1293, 1323, 1377, 1443, 1455, 1485
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 14 2009

Keywords

Comments

Composite numbers of the form A023202(k)+4, any k.
A087680 without the {7} [Proof: there are no 3 primes in arithmetic progression p, p+4, p+8, except p=3].
A164383 INTERSECT A164384; A087680 INTERSECT A002808.
If p=3*l+1, p+8 were divisible by 3, and if p=3*l+2, p+4 were divisible by 3. - R. J. Mathar, Aug 20 2009
All terms are divisible by 3. - Zak Seidov, Apr 22 2015

Examples

			a(1) = 5(prime)+4 = 13(prime)-4 = 9 (composite).
a(2) = 11(prime)+4 = 19(prime)-4 = 15 (composite).

Crossrefs

Cf. A002808, A023202, A087680.

Programs

  • Magma
    [n: n in [8..2000] | IsPrime(n+4) and IsPrime(n-4)]; // Vincenzo Librandi, Apr 22 2015
  • Mathematica
    Select[Range[8, 2000], PrimeQ[#+4] && PrimeQ[#-4] &] (* Vincenzo Librandi, Apr 22 2015 *)
Select[Range[9,5000],AllTrue[#+{4,-4},PrimeQ]&] (* Harvey P. Dale, Mar 23 2025 *)

Formula

a(n) = A023202(n+1)+4 = A087680(n+1). - Zak Seidov, Apr 22 2015

Extensions

65 removed, 337 changed to 237 etc. by R. J. Mathar, Aug 20 2009

A173250 Positive odd nonprimes of the form prime-10.

Original entry on oeis.org

1, 9, 21, 27, 33, 49, 51, 57, 63, 69, 87, 91, 93, 99, 117, 121, 129, 141, 147, 153, 169, 171, 183, 187, 189, 201, 213, 217, 219, 231, 247, 253, 259, 261, 267, 273, 297, 301, 303, 321, 327, 339, 343, 357, 363, 369, 387, 391, 399, 411, 423, 429, 447, 451, 453
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 14 2010

Keywords

Examples

			a(1)=1 because 11(prime)-10=1(positive odd nonprime); a(2)=9 because 19(prime)-10=9(positive odd nonprime).

Crossrefs

Cf. A000040, A141468, A164384.

Extensions

343 inserted by R. J. Mathar, Feb 21 2010

A173251 Positive odd nonprimes of the form prime-6.

Original entry on oeis.org

1, 25, 35, 55, 65, 77, 91, 95, 121, 125, 133, 143, 145, 161, 175, 185, 187, 205, 217, 221, 235, 245, 265, 275, 287, 301, 305, 325, 341, 343, 361, 377, 391, 395, 403, 413, 415, 425, 427, 437, 451, 455, 473, 481, 485, 493, 497, 515, 517, 535, 551, 565, 581, 595
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 14 2010

Keywords

Examples

			a(1)=1 because 7(prime)-6=1(positive odd nonprime); a(2)=25 because 31(prime)-6=25(positive odd nonprime).

Crossrefs

Cf. A000040, A141468, A164384.

Extensions

131 and 561 removed by R. J. Mathar, Mar 09 2010
Showing 1-4 of 4 results.

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