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.

A129215 Numbers m such that 9!*m -+ 1 are twin primes.

Original entry on oeis.org

3, 11, 22, 38, 52, 69, 125, 140, 154, 167, 169, 185, 198, 200, 205, 239, 299, 308, 335, 368, 376, 390, 405, 421, 482, 509, 574, 597, 610, 663, 684, 700, 701, 720, 763, 792, 795, 798, 840, 843, 855, 898, 907, 921, 954, 957
Offset: 1

Views

Author

Zak Seidov, Apr 03 2007

Keywords

Links

Crossrefs

Cf. A014574 (average of twin prime pairs), A127545 (multiples of 7 in A014574), A137877.
Numbers m such that (N!*m -+ 1) are twin primes: A129213 (N=7), A129214 (N=8), A129216 (N=10).

Programs

  • Magma
    [m:m in [1..1000]| IsPrime(Factorial(9)*m+1) and IsPrime(Factorial(9)*m-1)]; // Marius A. Burtea, Dec 29 2019
  • Mathematica
    s={};Do[m=362880k;If[PrimeQ[m-1]&&PrimeQ[m+1],AppendTo[s,k]],{k,1000}];s
With[{c=9!},Select[Range[1000],And@@PrimeQ[c*#+{1,-1}]&]] (* Harvey P. Dale, Aug 27 2013 *)

Formula

9!*a(n) are terms in A014574.

A137876 a(n) = (nextprime(18n)-previousprime(18n))/2.

Original entry on oeis.org

1, 3, 3, 1, 4, 1, 7, 5, 3, 1, 1, 6, 3, 3, 1, 5, 7, 7, 5, 4, 3, 4, 5, 1, 4, 6, 4, 3, 1, 9, 3, 3, 3, 3, 6, 3, 6, 4, 4, 4, 3, 3, 7, 5, 1, 1, 7, 7, 1, 10, 4, 4, 7, 3, 4, 6, 5, 5, 1, 9, 3, 4, 11, 1, 4, 3, 6, 3, 6, 9, 1, 3, 6, 17, 17, 3, 9, 5, 7, 4, 3, 5, 3, 6, 4, 3, 4, 7, 3, 1, 10, 10, 12, 12, 6, 5, 3, 9, 3, 6, 6
Offset: 1

Views

Author

Zak Seidov, Feb 19 2008

Keywords

Comments

a(n)=1 if 18n -/+ 1 are twin primes. Corresponding n's are in A137877.
Note that a(n) cannot be 2 (because, for arbitrary number m, if (6*m-1) is prime then (6*m+3) is not, and similarly, if (6*m+1) is prime then (6*m-3) is not). I conjecture that all other values are possible and a(n) == 0 (mod 3) are (much) more abundant.

Links

Crossrefs

Cf. A124519, A135023, A135368, A137877.

Programs

  • Magma
    [(NextPrime(18*n)-PreviousPrime(18*n))/2: n in [1..100]]; // Vincenzo Librandi, Apr 19 2015
  • Maple
    seq((nextprime(18*n)-prevprime(18*n))/2, n=1..100); # Robert Israel, Apr 19 2015
  • Mathematica
    Table[(NextPrime[18 n] - NextPrime[18 n, -1]) / 2, {n, 100}] (* Vincenzo Librandi, Apr 19 2015 *)
  • PARI
    a(n) = (nextprime(18*n) - precprime(18*n))/2; \\ Michel Marcus, Oct 13 2013

A137920 Numbers k such that 24*k-1 and 24*k+1 are twin primes.

Original entry on oeis.org

3, 8, 10, 13, 18, 25, 43, 48, 55, 62, 67, 78, 87, 88, 108, 112, 113, 125, 130, 132, 140, 147, 153, 157, 172, 178, 200, 207, 218, 220, 230, 235, 245, 265, 273, 283, 290, 297, 312, 315, 337, 343, 375, 385, 393, 405, 407, 417, 428, 465, 473, 493, 503, 510, 542
Offset: 1

Views

Author

Zak Seidov, Feb 23 2008

Keywords

Links

Crossrefs

Cf. A124519, A135023, A135368, A137876, A137877, A137919.

Programs

  • Magma
    [n: n in [1..600] | IsPrime(24*n+1) and IsPrime(24*n-1)] // Vincenzo Librandi, Feb 12 2018
  • Maple
    select(t -> isprime(24*t-1) and isprime(24*t+1), [$1..1000]); # Robert Israel, Feb 11 2018
  • Mathematica
    q=24; lst={}; Do[r=n*q; If[PrimeQ[r-1]&&PrimeQ[r+1], AppendTo[lst, n]], {n, 1, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 07 2008 *)
Select[Range[600], PrimeQ[24 # - 1] && PrimeQ[24 # + 1] &] (* Vincenzo Librandi, Feb 12 2018 *)
  • PARI
    isok(k) = isprime(24*k-1) && isprime(24*k+1); \\ Michel Marcus, Feb 12 2018

A137919 (Nextprime(24n)-previousprime(24n))/2.

Original entry on oeis.org

3, 3, 1, 4, 7, 5, 3, 1, 6, 1, 3, 5, 1, 3, 4, 3, 4, 1, 4, 4, 3, 9, 5, 3, 1, 6, 3, 6, 5, 4, 4, 4, 5, 5, 7, 7, 10, 4, 4, 7, 4, 6, 1, 5, 9, 3, 3, 1, 5, 4, 3, 6, 9, 3, 1, 17, 3, 9, 7, 4, 6, 1, 6, 6, 4, 7, 1, 5, 10, 12, 5, 5, 3, 9, 6, 4, 7, 1, 6, 9, 8, 11, 3, 3, 7, 3, 1, 1, 3, 4, 12, 3, 8, 8, 4, 6, 11, 3, 3, 6, 7, 6
Offset: 1

Views

Author

Zak Seidov, Feb 23 2008

Keywords

Comments

a(n)=1 if 24n -/+ 1 are twin primes.
Corresponding n's are in A137920.

Crossrefs

Cf. A124519, A135023, A135368, A137876, A137877, A137920.

Programs

  • Mathematica
    Table[(NextPrime[24n]-NextPrime[24n,-1])/2,{n,110}] (* Harvey P. Dale, Apr 15 2015 *)
  • PARI
    a(n) = (nextprime(24*n) - precprime(24*n))/2; \\ Michel Marcus, Oct 13 2013
Showing 1-4 of 4 results.

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