A177961 a(1)=2. Otherwise the average of the smallest prime divisors of 2n-1 and 2n+1.

2, 4, 6, 5, 7, 12, 8, 10, 18, 11, 13, 14, 4, 16, 30, 17, 4, 21, 20, 22, 42, 23, 25, 27, 5, 28, 29, 4, 31, 60, 32, 4, 36, 35, 37, 72, 38, 5, 43, 41, 43, 44, 4, 46, 48, 5, 4, 51, 50, 52, 102, 53, 55, 108, 56, 58, 59, 4, 5, 9, 7, 4, 66, 65, 67, 69, 5, 70, 138, 71, 7, 8, 4, 76, 150, 77, 4, 81

Offset: 1

Author

Vladimir Shevelev, May 16 2010, May 22 2010

Keywords

• nonn
• easy

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

Crossrefs

Cf. A177930, A177964, A177965, A177966.

Programs

Magma

[2] cat [1/2*(Min(PrimeFactors(2*n-1))+ Min(PrimeFactors(2*n+1))):n in [2..80]]; // Vincenzo Librandi, Feb 07 2016

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 *)

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

Formula

a(n) = (A090368(n)+A090368(n+1))/2. [R. J. Mathar, May 31 2010]

Extensions

More terms from R. J. Mathar, May 31 2010