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 A185446 Least prime such that whenever 2*a(n) = p+q with p and q prime, one has p,q > prime(n). 4
 3, 19, 19, 61, 61, 151, 151, 173, 173, 601, 677, 677, 677, 677, 691, 691, 691, 1321, 1321, 1321, 1321, 1321, 1321, 1321, 1321, 1321, 4801, 4801, 4801, 4801, 4801, 4801, 4801, 6781, 6781, 24001, 24001, 24001, 24001, 24001, 24001, 24001, 24001, 51869, 51869, 51869, 51869, 51869, 97151, 97151 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS D. Skordev et al, On the representation of some even numbers as sums of two prime numbers, in "primenumbers" yahoo group, Feb 02 2011. FORMULA a(n) = A185447(2^n-1) > prime(n). EXAMPLE For n=1, the least prime P such that 2P cannot be written as sum of two primes of which at least one is <= prime(1)=2, is obviously P=3. For n=2, we have a(2)=19 which is such that 2*19 can be written as 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. PROG (Sage) def A185446(n): ....pn = nth_prime(n) ....twoprimes = lambda n: ((p, n-p) for p in primes(n+1) if is_prime(n-p)) ....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 4 2011] CROSSREFS Sequence in context: A213602 A145688 A178985 * A172032 A043073 A022128 Adjacent sequences:  A185443 A185444 A185445 * A185447 A185448 A185449 KEYWORD nonn AUTHOR M. F. Hasler, Feb 03 2011 STATUS approved

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