A177983 a(1)=3. Otherwise the average of the least prime divisors of 2n-1 and 2n+3.

3, 5, 4, 9, 8, 7, 15, 11, 10, 21, 4, 13, 17, 17, 16, 18, 20, 4, 39, 23, 22, 45, 5, 25, 30, 4, 28, 32, 32, 31, 33, 35, 4, 69, 38, 37, 40, 41, 5, 81, 4, 43, 47, 5, 46, 6, 50, 4, 99, 53, 52, 105, 56, 55, 111, 4, 58, 6, 7, 5, 8, 65, 4, 129, 5, 67, 72, 71, 70, 75, 4, 7, 77, 77, 76, 78, 80, 4, 82, 83

Offset: 1

Author

Vladimir Shevelev, May 16 2010

Keywords

• nonn
• easy

Comments

Lim inf (n->infinity) (a(n)/n)=0.

If there exist infinitely many cousin primes (A023200), then lim sup (n->infinity) (a(n)/ n)=2.

Crossrefs

Cf. A020639, A177961.

Programs

Maple

A090368 := proc(n) A020639(2*n-1) ; end proc:
A177983 := proc(n) (A090368(n)+A090368(n+2)) /2 ; end proc:
seq(A177983(n),n=1..80) ; # R. J. Mathar, Oct 25 2010

Mathematica

Table[Mean[{FactorInteger[2n-1][[1,1]],FactorInteger[2n+3][[1,1]]}],{n,80}] (* Harvey P. Dale, Nov 08 2022 *)

PARI

a(n) = if (n==1, 3, (factor(2*n-1)[1,1] + factor(2*n+3)[1,1])/2); \\ Michel Marcus, Feb 08 2016

Formula

a(n) = (A090368(n)+A090368(n+2))/2 . [R. J. Mathar, Oct 25 2010]

Extensions

I corrected a(25). It should be 30 (not 31) Vladimir Shevelev, May 22 2010

More terms from R. J. Mathar, Oct 25 2010