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

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

Author

Zak Seidov, Feb 19 2008

Keywords

• nonn

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

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

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