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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 18 19:54 EST 2019. Contains 320262 sequences. (Running on oeis4.)