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Search: id:A145236
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| A145236 |
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a(n) is the least positive integer such that if p_n is the n-th prime then (ceil(sqrt(a(n)p_n)))^2-a(n)p_n is a perfect square |
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5
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| 2, 1, 1, 3, 5, 5, 9, 9, 13, 17, 19, 23, 25, 27, 31, 35, 41, 41, 47, 51, 51, 57, 61, 65, 73
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjectures: 1) for n>=2 the sequence does not decrease; 2) for n>1 a(n) is odd; 3) a(n) could be equal to a(n+1) only for twins: p_(n+1)-p_n=2 (although there exist also twins for which a(n)<a(n+1)).
All these conjectures are proved using the formula a(n)= p_n- 2floor(sqrt(2p_n))+2, n>1. See also A145701 and A145714. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Oct 18 2008]
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CROSSREFS
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Cf. A145016 A145022 A145023 A145047 A145048 A145049 A145050 A145215
Sequence in context: A058732 A060082 A102225 this_sequence A075248 A128325 A111528
Adjacent sequences: A145233 A145234 A145235 this_sequence A145237 A145238 A145239
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev (shevelev(AT)bgu.ac.il), Oct 05 2008, Oct 07 2008
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EXTENSIONS
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a(12)=23 (not 21). - Vladimir Shevelev (shevelev(AT)bgu.ac.il), Oct 16 2008
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