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.

A136720 Prime quadruples: 2nd term.

Original entry on oeis.org

7, 13, 103, 193, 823, 1483, 1873, 2083, 3253, 3463, 5653, 9433, 13003, 15643, 15733, 16063, 18043, 18913, 19423, 21013, 22273, 25303, 31723, 34843, 43783, 51343, 55333, 62983, 67213, 69493, 72223, 77263, 79693, 81043, 82723, 88813, 97843
Offset: 1

Views

Author

Enoch Haga, Jan 18 2008

Keywords

Comments

Primes p such that p-2, p+4, and p+6 are prime. Apart from the first term, a(n) = 13 (mod 30).

Examples

			The four terms in the first quadruple are 5,7,11,13 and in the 2nd 11,13,17,19. The four terms or members of each set must be simultaneously prime.

Links

Crossrefs

Cf. A007530, A090258, A136721.

Programs

  • Maple
    p2:= 0: p3:= 0: p4:= 0:
Res:= NULL: count:= 0:
while count < 100 do
  p1:= p2; p2:= p3; p3:= p4;
  p4:= nextprime(p4);
  if [p2-p1, p3-p2, p4-p3] = [2,4,2] then
     count:= count+1; Res:= Res, p2
  fi
od:
Res; # Robert Israel, Oct 11 2019
  • Mathematica
    lst={};Do[p0=Prime[n];If[PrimeQ[p2=p0+2], If[PrimeQ[p6=p0+6], If[PrimeQ[p8=p0+8], AppendTo[lst, p2]]]], {n, 12^4}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 22 2008 *)

Formula

a(n) = A007530(n)+2 = A136721(n)-4 = A090258(n)-6. - Robert Israel, Oct 11 2019

Extensions

Edited by Charles R Greathouse IV, Oct 11 2009

A050258 Number of "prime quadruplets" with largest member < 10^n.

Original entry on oeis.org

0, 2, 5, 12, 38, 166, 899, 4768, 28388, 180529, 1209318, 8398278, 60070590, 441296836, 3314576487, 25379433651, 197622677481
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

A "prime quadruplet" is a set of four primes {p, p+2, p+6, p+8}.
a(1) = 0 rather than 1 because the quadruple {2,3,5,7} does not have the official form.

Examples

			a(2) = 2 because there are two prime quadruplets with largest member less than 10^2, namely {5, 7, 11, 13} and {11, 13, 17, 19}.
a(3) = 5 because, in addition to the prime quadruplets mentioned above, below 10^3 we also have {101, 103, 107, 109}, {191, 193, 197, 199} and {821, 823, 827, 829}.

Links

Crossrefs

Cf. A007530.

Programs

  • Mathematica
    c = 1; Do[ Do[ If[ PrimeQ[ n ] && PrimeQ[ n + 2 ] && PrimeQ[ n + 6 ] && PrimeQ[ n + 8 ], c++ ], {n, 10^n + 1, 10^(n + 1), 10} ]; Print[ c ], {n, 1, 15} ] (* Weisstein *)
(* First run program for A090258 *) Table[Length[Select[A090258, # < 10^n &]], {n, 5}] (* Alonso del Arte, Aug 12 2012 *)

Extensions

a(16) (from Nicely link) added by Donovan Johnson, Jan 11 2011
a(17) added by Jonathan Webster, Jun 26 2018
a(1) changed to 0 at the suggestion of Harvey P. Dale. - N. J. A. Sloane, Sep 25 2019

A064974 Numbers k such that k-1, k-3, k-7 and k-9 are all prime.

Original entry on oeis.org

14, 20, 110, 200, 830, 1490, 1880, 2090, 3260, 3470, 5660, 9440, 13010, 15650, 15740, 16070, 18050, 18920, 19430, 21020, 22280, 25310, 31730, 34850, 43790, 51350, 55340, 62990, 67220, 69500, 72230, 77270, 79700, 81050, 82730, 88820
Offset: 1

Views

Author

Robert G. Wilson v, Oct 30 2001

Keywords

Links

Crossrefs

Cf. A090258.

Programs

  • Mathematica
    Select[Range[10^5], PrimeQ[ # - 1] && PrimeQ[ # - 3] && PrimeQ[ # - 7] && PrimeQ[ # - 9] &]
  • PARI
    { n=0; for (m=1, 10^9, if(isprime(m - 1) && isprime(m - 3) && isprime(m - 7) && isprime(m - 9), write("b064974.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 02 2009

A136721 Prime quadruples: 3rd term.

Original entry on oeis.org

11, 17, 107, 197, 827, 1487, 1877, 2087, 3257, 3467, 5657, 9437, 13007, 15647, 15737, 16067, 18047, 18917, 19427, 21017, 22277, 25307, 31727, 34847, 43787, 51347, 55337, 62987, 67217, 69497, 72227, 77267, 79697, 81047, 82727, 88817, 97847
Offset: 1

Views

Author

Enoch Haga, Jan 18 2008

Keywords

Comments

Primes p such that p-6, p-4, and p+2 are prime. Apart from the first term, a(n) = 17 (mod 30).
The members of each quadruple are twin primes when they are 1st and 2nd terms and when 3rd and 4th terms. When they are 2nd and 3rd terms they differ by 4.

Examples

			The four terms in the first quadruple are 5,7,11,13 and in the 2nd 11,13,17,19. The four terms or members of each set must be simultaneously prime.

Links

Crossrefs

Cf. A007530, A090258, A136720.

Programs

  • Maple
    p2:= 0: p3:= 0: p4:= 0:
Res:= NULL: count:= 0:
while count < 100 do
  p1:= p2; p2:= p3; p3:= p4;
  p4:= nextprime(p4);
  if [p2-p1, p3-p2, p4-p3] = [2, 4, 2] then
     count:= count+1; Res:= Res, p3
  fi
od:
Res; # Robert Israel, Oct 11 2019
  • Mathematica
    lst={};Do[p0=Prime[n];If[PrimeQ[p2=p0+2], If[PrimeQ[p6=p0+6], If[PrimeQ[p8=p0+8], AppendTo[lst, p6]]]], {n, 12^4}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 22 2008 *)

Formula

a(n) = A007530(n)+6 = A136720(n)+4 = A090258(n)-2. - Robert Israel, Oct 11 2019

Extensions

Edited by Charles R Greathouse IV, Oct 11 2009
Showing 1-4 of 4 results.

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