0,2

Let f(x) = A061357(x) be the number of primes p < x such that 2x-p is also prime. a(n) is the smallest positive integer x such that f(x) = n.

Or, least number m such that m can be expressed as the mean of two distinct primes in exactly n ways. Cf. A061357 = number of ways n can be expressed as the mean of two distinct primes, A120373 = number of ways the even integer 2n can be written as the sum of two primes for all even integers >6. - Zak Seidov (zakseidov(AT)yahoo.com), Sep 08 2006

For what values of n is a(n) > a(n+1)?

It seems that for n>7 n*log(n)*log(log(n)) < a(n) < 3n*log(n)*log(log(n)). Does lim n->infinity a(n)/n/log(n)/log(log(n)) exist ? - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 11 2002

a(1)=4 because 8 = 3+5 that is 8 can be expressed as the sum of two distinct primes by exactly 1 way,

a(2)=8 because 16 = 3+13 = 5+11 (2 ways),

a(3)=12 because 24 = 5+17 = 7+17 = 11+17 (3 ways),

a(4)=18 because 36 = 5+31 = 7+29 = 13+23 = 17+19 (4 ways), etc.

Starting with third term 12, all terms are multiples of 3.

f[x_] := Length[Select[2x-(Prime/@Range[PrimePi[x-1]]), PrimeQ]]; For[x=1, x<1000, x++, fx=f[x]; If[a[fx]>=0, Null, Null, a[fx]=x]]; a/@Range[0, 60]

Cf. A061357, A120373.

Sequence in context: A072473 A072715 A049621 this_sequence A082645 A111201 A045750

Adjacent sequences: A072508 A072509 A072510 this_sequence A072512 A072513 A072514

nonn

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2002

Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Aug 07 2002

Entry revised by njas, Sep 12 2006