A152522 a(n) is the least even number such that if p_i is the i-th prime then a(n)-p_i, i=1..n, are composite numbers.

6, 12, 30, 98, 98, 98, 98, 220, 308, 308, 556, 556, 556, 556, 992, 992, 992, 992, 992, 992, 2642, 2642, 2642, 2642, 2642, 2642, 5372, 5372, 5372, 5372, 5372, 5372, 5372, 7426, 7426, 7426, 7426, 7426, 7426, 43532, 43532, 43532, 43532, 43532, 43532

Offset

1,1

Comments

Conjecture (A. Granville, H. te Riele and J. van de Lune, 1989) Let, for even N, p=p(N) be the least prime such that N-p is prime as well. Then p(N)=O((log(N))^2log(log(N))). [Vladimir Shevelev, Dec 08 2008]

It is conjectured that a(n) >= prime(k+1) + 3. See Conjecture C p. 2 in Phong & Dongdong. - Michel Marcus, Aug 02 2017

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Andrew Granville, J. Van de Lune, and Herman te Riele, Checking the Goldbach Conjecture on a vector computer, Number Theory and Applications (1989), pp. 423-434.

Bui Minh Phong, Li Dongdong, Elementary problems which are equivalent to the Goldbach’s conjecture, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae 31 (2004) 33-37.

Mathematica

Bag={};
f[n_]:=NestList[NextPrime, 2, n];
GoldbachTest[n_?EvenQ, p_List]:=Block[{m=Length[p], i=1}, While[i<=m&&CompositeQ[n-p[[i]]], i+=1]; If[i>m, {0, 0}, {#, n-#}&[p[[i]]]]];
Do[n=4; While[(GoldbachTest[n, f[j]])!={0, 0}, {n=n+2}]; AppendTo[Bag, n], {j, 0, 44}]; Bag  (* Gilmar Rodriguez Pierluissi, Aug 23 2018 *)

Prog

(PARI) a(n)=my(P=prime(n)); forstep(k=6, 9e99, 2, forprime(p=3, P, if(isprime(k-p), next(2))); return(k)) \\ Charles R Greathouse IV, Sep 04 2011

Crossrefs

Cf. A025018.

Sequence in context: A015801 A073245 A119626 * A096356 A065992 A263587

Adjacent sequences: A152519 A152520 A152521 * A152523 A152524 A152525

Keyword

nonn

Author

Vladimir Shevelev, Dec 06 2008

Status

approved