OFFSET
1,1
COMMENTS
As n tends to infinity, we have 1) lim inf (a(n)/n)=0; 2) if there exist infinitely many twin primes, then lim sup (a(n)/n)=2, otherwise, lim sup (a(n)/n)=1.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
MAPLE
N:= 100: # to get a(1) to a(N)
S:= [1, seq(min(numtheory:-factorset(2*i-1)), i=2..N+1)]:
(S[2..-1]+S[1..-2])/2; # Robert Israel, Jul 31 2015
MATHEMATICA
Table[If[n == 1, 2, Mean[{FactorInteger[2 n - 1][[1, 1]], FactorInteger[2 n + 1][[1, 1]]}]], {n, 78}] (* Michael De Vlieger, Aug 02 2015 *)
PROG
(PARI) a(n) = if (n==1, 2, (vecmin(factor(2*n-1)[, 1]) + vecmin(factor(2*n+1)[, 1]))/2); \\ Michel Marcus, Feb 07 2016
(Magma) [2] cat [1/2*(Min(PrimeFactors(2*n-1))+ Min(PrimeFactors(2*n+1))):n in [2..80]]; // Vincenzo Librandi, Feb 07 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Shevelev, May 16 2010, May 22 2010
EXTENSIONS
More terms from R. J. Mathar, May 31 2010
STATUS
approved