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A353534
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a(n) is the least prime p such that the numerator of the sum of reciprocals of the 2*n+1 consecutive primes starting with p is a prime.
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3
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2, 2, 5, 197, 7, 157, 29, 41, 2, 599, 3, 13, 293, 19, 181, 59, 7, 1489, 557, 43, 11, 23, 2, 227, 191, 349, 179, 2, 103, 5479, 2, 7, 131, 971, 37, 2, 6917, 23, 1279, 10903, 593, 311, 239, 2711, 6277, 1669, 257, 293, 503, 1861, 13613, 11, 569, 719, 619, 709, 4523, 3, 3, 2549, 1361, 383, 3, 10193
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OFFSET
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1,1
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COMMENTS
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We use 2*n+1 consecutive primes rather than n because the numerator of the sum of reciprocals of an even number of odd primes is even.
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LINKS
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EXAMPLE
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a(3) = 5 because the sum of reciprocals of 2*3 + 1 = 7 primes starting with 5 is 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 = 24749279/37182145, and 24749279 is prime.
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MAPLE
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f:= proc(n) local i, k, v;
for k from 1 do
v:= numer(add(1/ithprime(i), i=k..k+2*n));
if isprime(v) then return ithprime(k) fi
od
end proc:
map(f, [$1..70]);
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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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