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A140112
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Primes of the form prime(x) + prime(x+1) + (prime(x+1)-prime(x))/2.
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1
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13, 37, 61, 71, 103, 131, 271, 277, 293, 311, 397, 457, 523, 541, 607, 743, 857, 1091, 1109, 1123, 1151, 1201, 1223, 1237, 1277, 1303, 1321, 1433, 1511, 1567, 1621, 1637, 1657, 1699, 1747, 1951, 2203, 2243, 2357, 2371, 2383, 2557, 2591, 2731, 2789, 2857
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OFFSET
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1,1
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LINKS
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EXAMPLE
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5+7+(7-5)/2=5+7+1=13
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MATHEMATICA
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a = {}; Do[p1 = Prime[n]; p2 = Prime[n + 1]; p = p1 + p2 + (p2 - p1)/2; If[PrimeQ[p], AppendTo[a, p]], {n, 10^2}]; a
Select[#[[1]]+#[[2]]+(#[[2]]-#[[1]])/2&/@Partition[Prime[ Range[ 500]], 2, 1], PrimeQ] (* Harvey P. Dale, Mar 16 2022 *)
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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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