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Search: id:A082612
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| A082612 |
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Numbers n such that ((n-1)^2+1)/2 and n^2+1 and ((n+1)^2+1)/2 are prime if n is even or (n-1)^2+1 and (n^2+1)/2 and (n+1)^2+1 are prime if n is odd. |
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+0
5
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| 3, 4, 5, 10, 15, 25, 170, 205, 570, 715, 780, 950, 1095, 1315, 1420, 1615, 2055, 2380, 2405, 2730, 2925, 3755, 3850, 4120, 4300, 4615, 4795, 5015, 5055, 5475, 5850, 6360
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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I believe this is an infinite sequence, though a proof seems to be still far off. 155-th term is 62910. There are probably infinitely many consecutive n^2+1 or (n^2+1)/2 primes. That is, n^2+1 and (n+2)^2+1 or (n^2+1)/2 and ((n+2)^2+1)/2 are both prime infinitely often.
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EXAMPLE
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a(4)=10 (9^2+1)/2=41 and 10^2+1=101 and (11^2+1)/2=61 are prime
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CROSSREFS
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Sequence in context: A135114 A079351 A058615 this_sequence A122413 A136366 A123820
Adjacent sequences: A082609 A082610 A082611 this_sequence A082613 A082614 A082615
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KEYWORD
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nonn
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AUTHOR
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Robin Garcia (verob99(AT)teleline.es), Sep 23 2004
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