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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.
Dimiter Skordev and others, On the representation of some even numbers as sums of two prime numbers, digest of 11 messages in primenumbers Yahoo group, Feb 2, 2011 - Feb 3, 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 the 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 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.
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 04 2011
CROSSREFS
Sequence in context: A178985 A357435 A266704 * A172032 A043073 A359314
KEYWORD
nonn
AUTHOR
M. F. Hasler, Feb 03 2011
STATUS
approved

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Last modified July 21 16:24 EDT 2024. Contains 374475 sequences. (Running on oeis4.)