A020481 Least p with p, q both prime, p+q = 2n.

2, 3, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 7, 3, 3, 5, 7, 3, 5, 3, 3, 5, 3, 5, 7, 3, 5, 7, 3, 3, 5, 7, 3, 5, 3, 3, 5, 7, 3, 5, 3, 5, 7, 3, 5, 7, 19, 3, 5, 3, 3, 5, 3, 3, 5, 3, 5, 7, 13, 11, 13, 19, 3, 5, 3, 5, 7, 3, 3, 5, 7, 11, 11, 3, 3, 5, 7, 3, 5, 7, 3, 5, 3, 5, 7, 3, 5, 7, 3, 3, 5, 7, 11, 11, 3, 3, 5, 3, 3, 5, 7

Offset: 2

Author

David W. Wilson

Keywords

• nonn

Comments

Essentially the same as A002373, which does not have the a(2) term. - T. D. Noe, Sep 24 2007

a(n) = A171637(n,1). - Reinhard Zumkeller, Mar 03 2014

Conjecture: a(n) ~ O(n^1/2). - Jon Perry, Apr 29 2014

Links

• Harry J. Smith, Table of n, a(n) for n = 2..20000
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A020482.

Programs

Haskell

a020481 n = head [p | p <- a000040_list, a010051' (2 * n - p) == 1]
-- Reinhard Zumkeller, Jul 07 2014, Mar 03 2014

Mathematica

a[n_] := For[p = 2, True, p = NextPrime[p], If[PrimeQ[2n-p], Return[p]]];
Table[a[n], {n, 2, 103}] (* Jean-François Alcover, Jul 31 2018  *)

PARI

A020481(n) = {local(np);np=1;while(!isprime(2*n-prime(np)),np++);prime(np)} \\ Michael B. Porter, Dec 11 2009

PARI

A020481(n)=forprime(p=1,n,isprime(2*n-p)&return(p)) \\ M. F. Hasler, Sep 18 2012

Python

from sympy import isprime, primerange
def A020481(n): return next(filter(lambda p:isprime((n<<1)-p),primerange(2*n))) # Chai Wah Wu, Nov 19 2024

Formula

a(n) = n - A047949(n). - Jason Kimberley, Oct 09 2012