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%I #29 Mar 08 2020 11:39:38
%S 3,19,19,61,61,151,151,173,173,601,677,677,677,677,691,691,691,1321,
%T 1321,1321,1321,1321,1321,1321,1321,1321,4801,4801,4801,4801,4801,
%U 4801,4801,6781,6781,24001,24001,24001,24001,24001,24001,24001,24001,51869,51869,51869,51869,51869,97151,97151
%N Least prime such that whenever 2*a(n) = p+q with p and q prime, one has p,q > prime(n).
%H D. Skordev et al., <a href="http://groups.yahoo.com/group/primenumbers/message/22543">On the representation of some even numbers as sums of two prime numbers</a>, in "primenumbers" Yahoo group, Feb 02 2011.
%H Dimiter Skordev and others, <a href="/A185446/a185446.txt">On the representation of some even numbers as sums of two prime numbers</a>, digest of 11 messages in primenumbers Yahoo group, Feb 2, 2011 - Feb 3, 2011.
%F a(n) = A185447(2^n-1) > prime(n).
%e For n=1, the least prime P such that 2P cannot be written as the sum of two primes of which at least one is <= prime(1)=2, is obviously P=3.
%e For n=2, we have a(2)=19, which is such that 2*19 can be written as the sum of primes only as 7+31 and 19+19, where no prime <= prime(2)=3 occurs. For smaller primes we have 2*17=3+31, 2*13=3+23, 2*11=3+19, 2*7=3+11, 2*5=3+5 (always using 3=prime(2)), and of course 3 and 2 are excluded, too.
%o (Sage)
%o def A185446(n):
%o pn = nth_prime(n)
%o twoprimes = lambda n: ((p, n-p) for p in primes(n+1) if is_prime(n-p))
%o return next(ap for ap in Primes() if all(p>pn and q>pn for p,q in twoprimes(2*ap))) # _D. S. McNeil_, Feb 04 2011
%K nonn
%O 1,1
%A _M. F. Hasler_, Feb 03 2011
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