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A343564
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a(n) is the sum of 2*n mod p for primes p such that 2*n-p is prime.
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2
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0, 0, 0, 5, 4, 7, 5, 10, 19, 18, 11, 32, 17, 25, 45, 24, 25, 56, 10, 45, 66, 32, 39, 96, 68, 55, 99, 59, 46, 148, 29, 104, 138, 49, 103, 162, 81, 112, 164, 91, 109, 260, 64, 105, 316, 115, 104, 235, 119, 202, 294, 188, 127, 319, 224, 251, 409, 177, 162, 500, 124, 181, 504, 135, 315, 437, 187, 271
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OFFSET
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1,4
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COMMENTS
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Conjecture: the only n for which a(n) <= n are 1, 2, 3, 5, 7, 11, 19, and 31.
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LINKS
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EXAMPLE
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For n=5, we have 2*n = 3+7 = 5+5, and a(5) = (10 mod 3)+(10 mod 5)+(10 mod 7) = 1+0+3 = 4.
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MAPLE
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N:= 1000: # for a(1)..a(N)
P:= select(isprime, [seq(i, i=3..2*N)]):
f:= proc(n) local m, Q, q;
m:= ListTools:-BinaryPlace(P, 2*n);
Q:= convert(P[1..m], set);
Q:= Q intersect map(t -> 2*n-t, Q);
add(2*n mod q, q = Q);
end proc:
map(f, [$1..N]);
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PROG
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(PARI) a(n) = my(p=2, s=0); forprime(p=2, 2*n, if (isprime(2*n-p), s += (2*n % p))); s; \\ Michel Marcus, Apr 20 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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