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A350399
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a(n) is the number of prime pairs (p,q) with p <= q, p+q = 2*n, and p*q mod (2*n) prime.
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3
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0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 1, 3, 1, 2, 4, 1, 2, 5, 2, 1, 4, 2, 2, 6, 3, 3, 4, 2, 4, 6, 2, 3, 5, 3, 4, 8, 3, 1, 9, 2, 3, 6, 3, 4, 5, 2, 4, 6, 4, 4, 8, 5, 2, 7, 3, 3, 10, 1, 2, 6, 2, 2, 6, 5, 4, 5, 3, 3, 11, 1, 4, 8, 4, 4, 7, 2, 5, 8, 4, 2, 7, 4, 1, 12, 4, 2, 9, 3, 4, 7, 2, 5
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OFFSET
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1,7
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COMMENTS
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Conjecture: a(n) > 0 for n >= 3.
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LINKS
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EXAMPLE
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a(7) = 2 because there are 2 such pairs, namely 14 = 3+13 = 7+7 with 3*13 == 5 (mod 14) and 7*7 == 7 (mod 14).
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MAPLE
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f:= proc(k) local P, i;
P:= select(t -> isprime(t) and isprime(2*k-t) and isprime(-t^2 mod (2*k)), [2, seq(i, i=3..k, 2)]);
nops(P);
end proc:
map(f, [$1..100]);
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MATHEMATICA
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a[n_] := Count[Select[Range[2, 2*n], PrimeQ], _?(# >= n && PrimeQ[2*n - #] && PrimeQ[Mod[#*(2*n - #), 2*n]] &)]; Array[a, 100] (* Amiram Eldar, Dec 28 2021 *)
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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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