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A097785
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Counterexamples to the conjecture that an even, prime-indexed triangular plus 1 equals a prime or that an odd, prime-indexed triangular minus 2 equals a prime.
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0
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497, 1771, 2279, 3161, 3487, 5149, 5357, 5993, 6439, 8129, 9451, 9731, 11477, 15049, 16469, 18337, 19901, 25879, 26333, 28681, 29159, 34717, 40187, 43069, 48517, 50401, 54947, 60379, 61073, 62479, 67529, 69749, 72011, 73537, 79001, 88829
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OFFSET
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1,1
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COMMENTS
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In the entry for 496, Wells remarks that it is the smallest counterexample to the conjecture that an even, prime-indexed triangular plus 1 equals a prime, since 497 is not prime.
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REFERENCES
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David Wells, The Penguin Dictionary of Curious and Interesting Numbers.
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LINKS
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MATHEMATICA
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tri[n_] := n(n + 1)/2; tp = Table[ tri[ Prime[n]], {n, 2, 85}]; f[n_] := If[ OddQ[n], n - 2, n + 1]; Select[f /@ tp, Not[ PrimeQ[ # ]] &]
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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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