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 1-5 of 5 results.

A384298 Primes p such that p + 4, p + 12 and p + 16 are also primes.

Original entry on oeis.org

7, 67, 97, 487, 757, 1567, 1597, 2377, 3907, 7687, 8677, 12097, 12907, 13147, 14407, 14767, 15667, 16057, 19417, 21487, 31177, 38317, 43777, 52567, 57637, 58897, 65167, 65827, 67477, 67927, 74857, 81547, 90007, 90187, 93967, 94777, 95467, 95617, 102547, 111427, 112237, 114757, 123817, 129277
Offset: 1

Views

Author

Alexander Yutkin, May 25 2025

Keywords

Comments

Initial members of prime quartets that correspond to the difference pattern [4, 8, 4].

Examples

			p=97: 97+4=101, 97+12=109, 97+16=113 —> prime quartet: (97, 101, 109, 113).

Links

Crossrefs

Cf. A000040, A001223.
Cf. A136162 [2, 4, 2], A052378 [4, 2, 4], A382810 [6, 4, 6].

Programs

  • Maple
    q:= n-> andmap(i-> isprime(n+4*i), [0,1,3,4]):
select(q, [7+30*i$i=0..4309])[];  # Alois P. Heinz, May 29 2025
  • Mathematica
    Select[Prime[Range[12099]],AllTrue[#+{4,12,16},PrimeQ]&] (* James C. McMahon, May 29 2025 *)

Formula

a(n) == 7 (mod 30).

A384299 Primes p such that p + 8, p + 12 and p + 20 are also primes.

Original entry on oeis.org

11, 59, 89, 389, 479, 1439, 1559, 1601, 2531, 2699, 3209, 3449, 3911, 5639, 5849, 7529, 8081, 8669, 10091, 12269, 12401, 12899, 13151, 14411, 14759, 17021, 19421, 21011, 21851, 22271, 23189, 25931, 26099, 28649, 28859, 31139, 31469, 33191, 33569, 36551, 39659, 40751, 42689, 43391, 43781, 44111
Offset: 1

Views

Author

Alexander Yutkin, May 25 2025

Keywords

Comments

Initial members of prime quartets that correspond to the difference pattern [8, 4, 8].

Examples

			p=89: 89+8=97, 89+12=101, 89+20=109 —> prime quartet: (89, 97, 101, 109).

Crossrefs

Cf. A000040, A001223.
Cf. A136162 [2, 4, 2], A052378 [4, 2, 4], A382810 [6, 4, 6].

Programs

  • Maple
    q:= n-> andmap(i-> isprime(n+4*i), [0,2,3,5]):
select(q, [5+6*i$i=1..7351])[];  # Alois P. Heinz, May 29 2025
  • Mathematica
    Select[Prime[Range[4591]],AllTrue[#+{8,12,20},PrimeQ]&] (* James C. McMahon, May 29 2025 *)

A384526 Primes p such that p + 6, p + 14 and p + 20 are also primes.

Original entry on oeis.org

17, 23, 47, 53, 83, 257, 263, 353, 443, 557, 587, 593, 977, 1103, 1217, 1277, 1283, 1433, 1607, 1973, 1997, 2267, 2657, 2693, 2837, 3527, 3617, 4007, 4637, 4643, 4937, 5393, 5807, 6197, 6257, 6323, 6353, 6977, 8693, 10253, 10847, 10973, 11483, 11807, 12143, 12497, 12953, 13613, 14537
Offset: 1

Views

Author

Alexander Yutkin, Jun 01 2025

Keywords

Comments

Initial members of prime quartets that correspond to the difference pattern [6, 8, 6].

Examples

			p=47: 47+6=53, 47+14=61, 47+20=67 —> prime quartet: (47, 53, 61, 67).

Crossrefs

Cf. A000040, A001223.
Cf. A140565 [6, 2, 6], A382810 [6, 4, 6].

Programs

  • Maple
    select(p -> andmap(isprime,[p, p + 6, p + 14, p + 20]), [seq(i,i=5 .. 20000, 6)]); # Robert Israel, Jun 01 2025
  • Mathematica
    Select[Prime[Range[1700]], PrimeQ[#+6]&&PrimeQ[#+14]&&PrimeQ[#+20] &] (* Stefano Spezia, Jun 01 2025 *)

Formula

a(n) == 5 (mod 6). - Hugo Pfoertner, Jun 01 2025

A384528 Primes p such that p + 6, p + 12, p + 16, p + 22 and p + 28 are also primes.

Original entry on oeis.org

31, 151, 2671, 20101, 128461, 198811, 297601, 307261, 350431, 354301, 531331, 560221, 585721, 649771, 813991, 1049821, 1141081, 1553401, 1616611, 1763401, 2032621, 2126611, 2349301, 2628811, 2874721, 2967331, 3014371, 3414211, 3441931, 3491071, 3677341, 3699181, 4192261, 4941241, 4951621
Offset: 1

Views

Author

Alexander Yutkin, Jun 01 2025

Keywords

Comments

Initial members of prime sextuples that correspond to the difference pattern [6, 6, 4, 6, 6].

Examples

			p=151: 151+6=157, 151+12=163, 151+16=167, 151+22=173, 151+28=179 —> prime sextuple: (151, 157, 163, 167, 173, 179).

Crossrefs

Cf. A000040, A001223.
Cf. A023241 [6, 6], A382810 [6, 4, 6].

Programs

  • Mathematica
    Select[Prime[Range[350000]],PrimeQ[#+6]&&PrimeQ[#+12]&&PrimeQ[#+16]&&PrimeQ[#+22]&&PrimeQ[#+28] &] (* Stefano Spezia, Jun 01 2025 *)

Formula

a(n) == 1 (mod 30). - Hugo Pfoertner, Jun 01 2025

A383393 Primes p such that p + 2, p + 8, p + 12, p + 18 and p + 20 are also primes.

Original entry on oeis.org

11, 5639, 5849, 45119, 51419, 54401, 88799, 130631, 165701, 229751, 284729, 321311, 626609, 797549, 855719, 883229, 1068701, 1128761, 1146779, 1178699, 1652879, 1978421, 2253479, 2254781, 2269439, 2453441, 3154421, 3216119, 4046291, 4583849, 5050679, 5387729
Offset: 1

Views

Author

Alexander Yutkin, Apr 25 2025

Keywords

Comments

Initial members of prime sextuples that correspond to the difference pattern [2, 6, 4, 6, 2].

Examples

			p = 5639: 5639 + 2 = 5641, 5639 + 8 = 5647, 5639 + 12 = 5651, 5639 + 18 = 5657, 5639 + 20 = 5659 -> prime sextuple: (5639, 5641, 5647, 5651, 5657, 5659).

Crossrefs

Cf. A000040, A001223.
Cf. A382810 [6, 4, 6], A022008 [4, 2, 4, 2, 4].

Programs

  • Mathematica
    Select[Prime[Range[373583]], AllTrue[#+{2,8,12,18,20}, PrimeQ]&] (* James C. McMahon, May 02 2025 *)
Showing 1-5 of 5 results.

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