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A187129
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Consider all pairs of primes (p,q) with p+q = 2n, p <= q; a(n) is the sum of all the q's.
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10
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2, 3, 5, 12, 7, 18, 24, 24, 30, 47, 49, 55, 40, 59, 48, 100, 102, 50, 89, 120, 109, 136, 181, 158, 117, 199, 133, 170, 252, 133, 261, 300, 98, 267, 324, 279, 303, 419, 244, 303, 494, 345, 260, 593, 302, 343, 503, 207, 452, 612, 399, 488, 668, 526, 619, 872, 574, 540, 1082, 352, 475, 920, 273, 691, 865, 598, 523, 822, 725, 864, 1211
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OFFSET
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2,1
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LINKS
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FORMULA
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EXAMPLE
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2*5 = 10 can be expressed as the sum of two primes in two ways: 3+7 and 5+5, so a(5) = 7+5 = 12.
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MAPLE
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with(numtheory); a:=n-> sum( (2*n-i)*( ((pi(i) - pi(i-1)) * (pi(2*n-i) - pi(2*n-i-1))) ), i = 1..n ); seq(a(k), k=1..100); # Wesley Ivan Hurt, Jan 20 2013
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MATHEMATICA
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Table[Total[Select[IntegerPartitions[2*n, {2}], AllTrue[#, PrimeQ]&][[All, 1]]], {n, 2, 100}] (* Harvey P. Dale, Aug 09 2020 *)
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PROG
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(PARI) a(n) = my(s=0); forprime(p=1, n, if (isprime(2*n-p), s += 2*n-p)); s; \\ Michel Marcus, Apr 29 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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