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A240718
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Number of decompositions of 2n into an unordered sum of two primes, one of the two primes less than sqrt(2n-2).
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2
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0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 0, 1, 0, 0, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 3, 3, 1, 1, 2, 2, 2, 2, 2
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OFFSET
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1,17
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LINKS
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EXAMPLE
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For n = 7, the a(7) = 1 solution is 2*7 = 3 + 11 = 7 + 7; one of these pairs, 3 + 11, contains a number less than sqrt(2*7 - 2).
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MAPLE
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P:= NULL: A[1]:= 0: nextp:= 2:
for n from 2 to 100 do
while nextp^2 < 2*n-2 do
P:= P, nextp;
nextp:= nextprime(nextp);
od;
A[n]:= numboccur(true, map(t -> isprime(2*n-t), [P]))
od:
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PROG
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(PARI)
a(n)=sum(i=2, primepi(floor(sqrt(2*n-2))), isprime(2*n-prime(i))) \\ Lear Young, Apr 11 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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