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A185446
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Least prime such that whenever 2*a(n) = p+q with p and q prime, one has p,q > prime(n).
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4
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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
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..50.
D. Skordev et al, On the representation of some even numbers as sums of two prime numbers, in "primenumbers" yahoo group, Feb 02 2011.
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FORMULA
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a(n) = A185447(2^n-1) > prime(n).
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EXAMPLE
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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.
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PROG
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(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]
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CROSSREFS
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Sequence in context: A213602 A145688 A178985 * A172032 A043073 A022128
Adjacent sequences: A185443 A185444 A185445 * A185447 A185448 A185449
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler, Feb 03 2011
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STATUS
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approved
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