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A092938
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a(n) = least prime p such that 2*prime(n) - p is prime.
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3
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2, 3, 3, 3, 3, 3, 3, 7, 3, 5, 3, 3, 3, 3, 5, 3, 5, 13, 3, 3, 7, 7, 3, 5, 3, 3, 7, 3, 7, 3, 3, 5, 3, 7, 5, 19, 3, 13, 3, 29, 5, 3, 3, 3, 5, 19, 3, 3, 5, 19, 3, 11, 3, 3, 5, 3, 17, 19, 7, 5, 3, 17, 7, 3, 7, 3, 3, 13, 3, 7, 5, 17, 7, 3, 7, 5, 5, 7, 5, 7, 11, 3, 3, 3, 19, 3, 11, 3, 3, 7, 5, 5, 3, 5, 7, 23, 5, 3
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OFFSET
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1,1
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COMMENTS
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a(n) = least prime p such that prime(n) = (p+q)/2, where q is also prime.
a(n) <= prime(n). Conjecture: a(n) = prime(n) only for n = 1 and 2.
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LINKS
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EXAMPLE
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2*prime(8) = 38; 38 - 2 = 36, 38 - 3 = 35, 38 - 5 = 33 are composite, but 38 - 7 = 31 is prime. Hence a(8) = 7.
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MAPLE
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f:= proc(n) local pn, p;
pn:= ithprime(n);
p:= 1;
do
p:= nextprime(p);
if isprime(2*pn-p) then return p fi
od
end proc:
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MATHEMATICA
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a[n_] := Module[{p, q = Prime[n]}, For[p = 2, True, p = NextPrime[p], If[PrimeQ[2q-p], Return[p]]]];
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PROG
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(PARI) {for(n=1, 98, k=2*prime(n); p=2; while(!isprime(k-p), p=nextprime(p+1)); print1(p, ", "))} \\ Klaus Brockhaus, Dec 23 2006
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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