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Least even a(n) > 2 not representable as a sum of two of the first n primes. From Goldbach conjecture.
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%I #34 Jan 14 2025 16:11:23

%S 6,8,12,16,20,28,32,40,44,44,56,64,76,76,92,92,92,110,116,116,136,136,

%T 148,164,174,182,188,188,220,224,232,242,242,256,260,272,272,292,292,

%U 292,332,350,350,368,368,368,400,400,412,412,436,442,442,476,476,476

%N Least even a(n) > 2 not representable as a sum of two of the first n primes. From Goldbach conjecture.

%C a(n)<=2p(n)+2, where p(n) is the n-th prime.

%C The only even prime number, 2, is not able to be represented as a sum of two primes. - _Lei Zhou_, Apr 09 2014

%H Lei Zhou, <a href="/A090259/b090259.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5)=20 since {2,3,5,7,11} can't represent 20 as a sum of two primes.

%t a = {}; c = 6; Table[p = Prime[n]; Do[q = Prime[k]; If[sum = p + q; ! MemberQ[a, sum], AppendTo[a, sum]], {k, PrimePi[NextPrime[c - p, -1]], n}]; While[MemberQ[a, c], c = c + 2]; c, {n, 1, 100}] (*_Lei Zhou_, Apr 09 2014*)

%Y Cf. A002372.

%K nonn

%O 1,1

%A Ed T. Prothro (prothro(AT)compuserve.com), Jan 24 2004

%E Flaw in the title fixed by _Lei Zhou_, Apr 09 2014