A137876 - OEIS

%I #25 Sep 08 2022 08:45:33

%S 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,

%T 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,

%U 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

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

%C a(n)=1 if 18n -/+ 1 are twin primes. Corresponding n's are in A137877.

%C 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.

%H Zak Seidov, <a href="/A137876/b137876.txt">Table of n, a(n) for n = 1..10000</a>

%p seq((nextprime(18*n)-prevprime(18*n))/2, n=1..100); # _Robert Israel_, Apr 19 2015

%t Table[(NextPrime[18 n] - NextPrime[18 n, -1]) / 2, {n, 100}] (* _Vincenzo Librandi_, Apr 19 2015 *)

%o (PARI) a(n) = (nextprime(18*n) - precprime(18*n))/2; \\ _Michel Marcus_, Oct 13 2013

%o (Magma) [(NextPrime(18*n)-PreviousPrime(18*n))/2: n in [1..100]]; // _Vincenzo Librandi_, Apr 19 2015

%Y Cf. A124519, A135023, A135368, A137877.

%K nonn

%O 1,2

%A _Zak Seidov_, Feb 19 2008