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Search: id:A097785
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| A097785 |
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Counterexamples to 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
1
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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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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Cf. A096333.
Sequence in context: A013685 A108157 A062676 this_sequence A064255 A067917 A093249
Adjacent sequences: A097782 A097783 A097784 this_sequence A097786 A097787 A097788
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KEYWORD
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nonn
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AUTHOR
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Alonso Del Arte (alonso.delarte(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 24 2004
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