A135368 -id:A135368 - cp's OEIS frontend

A137877 Numbers k such that 18k - 1 and 18k + 1 are twin primes.

1, 4, 6, 10, 11, 15, 24, 29, 45, 46, 49, 59, 64, 71, 90, 104, 111, 116, 119, 126, 130, 144, 155, 165, 176, 181, 185, 196, 199, 204, 214, 225, 231, 235, 241, 249, 251, 266, 274, 276, 279, 301, 314, 319, 325, 326, 350, 364, 365, 370, 386, 396, 406, 416, 420, 431

Offset: 1

Zak Seidov, Feb 19 2008

nonn

			1 is in the sequence since 18*1 - 1 = 17 and 18*1 + 1 = 19 are twin primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A124519, A135023, A135368, A137876.

q=18; 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 *)

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

Zak Seidov, Feb 19 2008

nonn

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.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A124519, A135023, A135368, A137877.

[(NextPrime(18*n)-PreviousPrime(18*n))/2: n in [1..100]]; // Vincenzo Librandi, Apr 19 2015

seq((nextprime(18*n)-prevprime(18*n))/2, n=1..100); # Robert Israel, Apr 19 2015

Table[(NextPrime[18 n] - NextPrime[18 n, -1]) / 2, {n, 100}] (* Vincenzo Librandi, Apr 19 2015 *)

a(n) = (nextprime(18*n) - precprime(18*n))/2; \\ Michel Marcus, Oct 13 2013

A137920 Numbers k such that 24k-1 and 24k+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

Zak Seidov, Feb 23 2008

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

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

[n: n in [1..600] | IsPrime(24*n+1) and IsPrime(24*n-1)] // Vincenzo Librandi, Feb 12 2018

select(t -> isprime(24*t-1) and isprime(24*t+1), [$1..1000]); # Robert Israel, Feb 11 2018

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 *)

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

Zak Seidov, Feb 23 2008

nonn

a(n)=1 if 24n -/+ 1 are twin primes.

Corresponding n's are in A137920.

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

Table[(NextPrime[24n]-NextPrime[24n,-1])/2,{n,110}] (* Harvey P. Dale, Apr 15 2015 *)

a(n) = (nextprime(24*n) - precprime(24*n))/2; \\ Michel Marcus, Oct 13 2013

cp's OEIS Frontend

A137877 Numbers k such that 18*k - 1 and 18*k + 1 are twin primes.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

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

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

A137877 Numbers k such that 18k - 1 and 18k + 1 are twin primes.

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