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A140199
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a(n) = the number of pairs of (not necessarily distinct) positive integers j and k where j <= n and k <= n such that k+j is prime.
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1
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1, 2, 3, 5, 6, 8, 10, 12, 15, 19, 22, 26, 29, 32, 36, 41, 45, 49, 53, 57, 62, 68, 73, 79, 85, 91, 98, 105, 111, 118, 125, 132, 139, 147, 155, 164, 173, 182, 191, 201, 210, 220, 229, 238, 248, 258, 267, 276, 286, 296, 307, 319, 330, 342, 355, 368, 382, 396, 409, 422
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = sum{k=1 to n} A108954(k). (A108954(n) = pi(2n)-pi(n), where pi(n) is the number of primes that are <= n). a(n) = A071917(n)+1.
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EXAMPLE
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For n = 4 there are 5 pairs of positive integers, each <= n=4, that sum to a prime: 1+1=2, 1+2=3, 2+3=5, 1+4=5 and 3+4=7.
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MAPLE
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MATHEMATICA
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Table[Count[Union[Sort/@Tuples[Range[n], {2}]], _?(PrimeQ[Total[#]]&)], {n, 60}] (* Harvey P. Dale, Mar 21 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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EXTENSIONS
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STATUS
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approved
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