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A057324
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First member of a prime triple in a p^2 + p - 1 progression.
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2
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2, 3, 11, 13, 53, 131, 233, 241, 281, 569, 659, 691, 761, 881, 1693, 2063, 2411, 2521, 2551, 2663, 2729, 2741, 2861, 3089, 4021, 4159, 4201, 4243, 4423, 4793, 6091, 7103, 7229, 7369, 7753, 7829, 8053, 8641, 8669, 9041, 9059, 9539, 9649, 9769, 10513
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OFFSET
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1,1
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COMMENTS
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There exist no such triples of the form p^2 + p + 1 because each third member is always divisible by 3.
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LINKS
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EXAMPLE
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2 -> 2^2+2-1 = 5 -> 5^2+5-1 = 29 hence the prime triple (2,5,29).
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MATHEMATICA
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fmpQ[n_]:=AllTrue[NestList[#^2+#-1&, n, 2], PrimeQ]; Select[Prime[Range[ 1300]], fmpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 08 2019 *)
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PROG
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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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