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.

A090161 A023219 indexed by A000040.

Original entry on oeis.org

3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 18, 22, 23, 25, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 42, 44, 45, 47, 50, 51, 52, 55, 56, 58, 62, 65, 69, 72, 74, 75, 77, 79, 82, 83, 86, 87, 89, 91, 93, 96, 97, 99, 100, 101, 102, 104, 105, 108, 109, 110, 111, 117, 119, 120, 122, 123
Offset: 1

Views

Author

Ray Chandler, Nov 28 2003

Keywords

Crossrefs

Cf. A023219, A088555, A088561.

Formula

a(n) = k such that A000040(k) = A023219(n).
a(n) = A000720(A023219(n)). - Michel Marcus, Aug 06 2021

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

A088664 Duplicate of A023219.

Original entry on oeis.org

5, 7, 11, 13, 19, 29, 37, 41, 47, 53, 61, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 149
Offset: 1

Views

Author

Keywords

A088555 Primes of the form 5*p + 6 where p is a prime.

Original entry on oeis.org

31, 41, 61, 71, 101, 151, 191, 211, 241, 271, 311, 401, 421, 491, 521, 541, 571, 641, 661, 691, 701, 751, 761, 821, 911, 971, 991, 1061, 1151, 1171, 1201, 1291, 1321, 1361, 1471, 1571, 1741, 1801, 1871, 1901, 1951, 2011, 2111, 2161, 2221, 2251, 2311, 2341
Offset: 1

Views

Author

Ray Chandler, Nov 28 2003

Keywords

Comments

Primes arising in A023219.
Subsequence of A030430.

Links

Crossrefs

Cf. A023219, A030430, A088561, A090161.

Programs

  • Magma
    [5*p+6: p in PrimesUpTo(600)| IsPrime(5*p+6)]; // Vincenzo Librandi, May 19 2017
  • Mathematica
    6 + 5 Select[Prime[Range[200]], PrimeQ[5 # + 6] &] (* Vincenzo Librandi, May 19 2017 *)
  • PARI
    forprime(p=2,500,my(pp=5*p+6);if(isprime(pp),print1(pp,", "))) \\ Hugo Pfoertner, Aug 06 2021

Formula

a(n) = 5*A023219(n) + 6.

Extensions

Name clarified by Jinyuan Wang, Aug 06 2021

A023285 Primes that remain prime through 3 iterations of function f(x) = 5x + 6.

Original entry on oeis.org

7, 79, 181, 233, 359, 401, 449, 1009, 1093, 1259, 1303, 1373, 1511, 1931, 2011, 2339, 2477, 3019, 3691, 4349, 4409, 5417, 5879, 6301, 6553, 6637, 7079, 8329, 9127, 9137, 10303, 10499, 11579, 12391, 13259, 14251, 15101, 15107, 15217, 15329, 15527, 15679
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+6, 25*p+36 and 125*p+186 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023219, A023254, and of A081759.

Programs

  • Magma
    [n: n in [1..150000] | IsPrime(n) and IsPrime(5*n+6) and IsPrime(25*n+36) and IsPrime(125*n+186)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    p3Q[n_]:=And@@PrimeQ/@NestList[5#+6&,n ,3]; Select[Prime[Range[2000]],p3Q] (* Harvey P. Dale, Feb 20 2011 *)

A088561 A088555 indexed by A000040.

Original entry on oeis.org

11, 13, 18, 20, 26, 36, 43, 47, 53, 58, 64, 79, 82, 94, 98, 100, 105, 116, 121, 125, 126, 133, 135, 142, 156, 164, 167, 178, 190, 193, 197, 210, 216, 218, 233, 248, 271, 279, 286, 291, 297, 305, 318, 326, 331, 335, 344, 347, 362, 369, 374, 381, 395, 400, 406
Offset: 1

Views

Author

Ray Chandler, Nov 28 2003

Keywords

Comments

Subset of A049511.

Crossrefs

Cf. A023219, A049511, A088555, A090161.

Formula

a(n) = k such that A000040(k) = A088555(n).
a(n) = A000720(A088555(n)). - Michel Marcus, Aug 06 2021

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

A023315 Primes that remain prime through 4 iterations of function f(x) = 5*x + 6.

Original entry on oeis.org

79, 401, 1259, 2477, 3019, 4409, 10303, 15679, 20509, 24499, 34127, 43987, 44389, 53101, 66359, 71287, 74857, 81097, 85903, 90803, 93053, 102811, 103231, 104999, 112601, 125453, 132533, 144731, 156347, 157793, 160817, 161839, 163981, 170641
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+6, 25*p+36, 125*p+186 and 625*p+936 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023219, A023254, A023285, and A081759.

Programs

  • Magma
    [n: n in [1..1000000] | IsPrime(n) and IsPrime(5*n+6) and IsPrime(25*n+36) and IsPrime(125*n+186) and IsPrime(625*n+936)]; // Vincenzo Librandi, Aug 04 2010

Formula

a(n) == 9 or 13 (mod 14). - John Cerkan, Oct 07 2016

A340444 a(n) is the least prime of the form p*q + p*r + q*r where p is the n-th prime and q and r are primes < p, or 0 if there are none.

Original entry on oeis.org

0, 0, 31, 41, 61, 71, 151, 101, 199, 151, 227, 191, 211, 311, 241, 271, 487, 311, 479, 653, 521, 401, 421, 727, 491, 823, 521, 541, 773, 571, 641, 661, 691, 701, 751, 761, 1109, 821, 2039, 1399, 1447, 911, 1543, 971, 991, 1607, 1061, 1571, 1831, 1151, 1171, 1201, 1697, 2273, 1291, 1321, 2711
Offset: 1

Views

Author

Robert Israel, Jan 07 2021

Keywords

Comments

If prime(k) is in A023219, a(k) = 5*prime(k)+6.

Examples

			a(7) = 151 because prime(7) = 17, and 151 = 17*3+17*5+3*5 is the least prime of the form 17*p + 17*q + p*q.

Links

Crossrefs

Cf. A023219, A340439.

Programs

  • Maple
    f:= proc(n) local p,L,i,j,t;
  p:= ithprime(n);
  L:= sort([seq(seq((ithprime(i)+p)*(ithprime(j)+p)-p^2, i=1..j-1),j=2..n-1)]);
  for t in L do if isprime(t) then return t fi od:
  0
end proc:
A:= map(f, [$1..100]);
  • Python
    from sympy import isprime, prime
def aupto(nn):
  alst, plst = [0 for i in range(nn)], [prime(i+1) for i in range(nn)]
  for n in range(1, nn+1):
    p = plst[n-1]
    t = ((p, plst[i], plst[j]) for i in range(n-2) for j in range(i+1, n-1))
    for s in sorted(p*q + p*r + q*r for p, q, r in t):
      if isprime(s): alst[n-1]=s; break
  return alst
print(aupto(57)) # Michael S. Branicky, Jan 07 2021

A023343 Primes that remain prime through 5 iterations of function f(x) = 5x + 6.

Original entry on oeis.org

79, 34127, 345431, 549089, 669937, 703663, 948593, 978749, 999007, 1251329, 1255333, 1279133, 1500277, 1517413, 1525421, 1642769, 1670629, 1688101, 1727161, 1770127, 2152159, 2161343, 2328517, 2622167, 2745451, 2786681, 2837557, 3281777
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 5*p+6, 25*p+36, 125*p+186, 625*p+936 and 3125*p+4686 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A023219, A023254, A023285, A023315, and A081759.

Programs

  • Magma
    [n: n in [1..10000000] | IsPrime(n) and IsPrime(5*n+6) and IsPrime(25*n+36) and IsPrime(125*n+186) and IsPrime(625*n+936) and IsPrime(3125*n+4686)] // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    Select[Prime[Range[250000]],And@@PrimeQ[Rest[NestList[5#+6&,#,5]]]&] (* Harvey P. Dale, Jan 03 2014 *)

Formula

a(n) == 9 (mod 14). - John Cerkan, Oct 20 2016

A106079 Primes p such that 5*p + 6 and 6*p + 5 are primes.

Original entry on oeis.org

7, 11, 13, 29, 37, 41, 79, 83, 97, 107, 113, 137, 139, 151, 163, 181, 193, 197, 239, 263, 347, 373, 389, 401, 421, 431, 443, 449, 487, 503, 541, 557, 643, 653, 701, 821, 839, 883, 911, 1033, 1051, 1093, 1129, 1163, 1201, 1217, 1259, 1283, 1303, 1373
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Links

Crossrefs

Intersection of A023219 and A023221. - Michel Marcus, Nov 06 2018

Programs

  • Magma
    [p: p in PrimesUpTo(5000)|IsPrime(5*p+6) and IsPrime(6*p+5)] // Vincenzo Librandi, Jan 30 2011
  • Maple
    select(n -> isprime(n) and isprime(5*n+6) and isprime(6*n+5), [seq(2*i+1,i=1..1000)]); # Robert Israel, Aug 04 2014
  • Mathematica
    Select[Prime[Range[220]], PrimeQ[6#+5]&&PrimeQ[5#+6]&]
  • PARI
    forprime(p=1,10^4,if(isprime(5*p+6)&&isprime(6*p+5),print1(p,", "))) \\ Derek Orr, Aug 04 2014
Showing 1-9 of 9 results.

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