1,2

a(n) for n>1 is prime. Further the upper part of at least n in i well-ordered prime factors p_i(n) of the numerator of 2^(1-2 n^2) n binomial(2 n^2, n^2) (A285388(n)) consists of only single factors which form especially a complete part of the prime numbers p with 3 < 2(n-1)^2 < p <= a(n) < 2n^2. Thus the complete union of {2,3} and {p_i(m)} for m from 2 to n gives all prime numbers p <= a(n).

Alternative definitions are "Greatest prime factor of the numerator of 2^(1-2 n^2) n binomial(2 n^2, n^2)". and "Greatest prime factor of numerator of sum{k=0..n^2-1}(binomial(2k,k)/4^k)/n". - David A. Corneth, Apr 26 2017

a(n) = A006530(A285388(n)).

Table[Last[FactorInteger[Numerator[2^(1-2 n^2) n Binomial[2 n^2, n^2]]][[All, 1]]], {n, 1, 30}]

(PARI) a(n) = my(f = factor(sum(k = 0, n^2-1, (binomial(2*k, k)/4^k))/n)[, 1]); f[#f] \\ David A. Corneth, Apr 25 2017

(PARI) a(n) = if(n==1, 1, my(f=factor(n*binomial(2*n^2, n^2))[, 1]); f[#f]) \\ David A. Corneth, Apr 26 2017

(PARI) a(n) = if(n==1, return(1)); my(i=2*n^2); while(!isprime(i), i--); i \\ David A. Corneth, Apr 26 2017

Cf. A006530, A285388, A000040 (prime numbers), A285786 (Number of primes in interval).

Sequence in context: A001123 A094080 A046118 * A120092 A130284 A056220

Adjacent sequences: A285735 A285736 A285737 * A285739 A285740 A285741

nonn,easy

Ralf Steiner, Apr 25 2017

a(31)-a(49) from David A. Corneth, Apr 25 2017

New name from David A. Corneth, Apr 26 2017

approved