A007944 a(n) is the largest even number k such that 6, 8, ..., k are sums of 2 of first n odd primes.

6, 10, 14, 18, 26, 30, 38, 42, 42, 54, 62, 74, 74, 90, 90, 90, 108, 114, 114, 134, 134, 146, 162, 172, 180, 186, 186, 218, 222, 230, 240, 240, 254, 258, 270, 270, 290, 290, 290, 330, 348, 348, 366, 366, 366, 398, 398, 410, 410, 434, 440, 440, 474, 474, 474, 474, 474, 522

Offset: 1

Author

R. Muller

Keywords

• nonn
• easy

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996, 50 pages. See page 20.
• K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996, 50 pages. [Cached copy] See page 20.
• F. Smarandache, Only Problems, Not Solutions!

Programs

Mathematica

Table[tot = Total /@ Tuples[Prime[Range[2, n + 1]], 2]; lim = Last@tot; First[Select[Range[6, lim, 2], ! MemberQ[tot, #] &] - 2, lim], {n, 58}] (* Robert Price, Apr 26 2025 *)

PARI

first(n) = {n+=3; my(fnf = 6, pr = primes(n), found = vector(pr[n]), res = vector(n-3), start = 2); for(i = 2, n-2, for(j = start, i, found[(pr[i]+pr[j])>>1] = 1);for(j = fnf>>1, pr[n], if(found[j]==0, fnf = j<<1; break)); while(pr[start] + pr[i+1]fnf, start--); res[i-1]=fnf-2); res} \\ David A. Corneth, Jul 06 2017

Formula

a(n) << n log n. - Charles R Greathouse IV, Sep 19 2012

More specifically, a(n) <= 2*prime(n+1). On the Goldbach conjecture a(n) >= prime(n+1) + 3. - Charles R Greathouse IV, Dec 09 2014

Extensions

More terms from David W. Wilson