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Search: id:A111058
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| A111058 |
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Numbers n such that the average of the first n Lucas numbers is an integer. |
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1
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| 1, 2, 8, 12, 20, 24, 48, 60, 68, 72, 92, 96, 120, 140, 144, 188, 192, 200, 212, 216, 240, 288, 300, 332, 336, 360, 384, 428, 432, 440, 452, 480, 500, 548, 576, 600, 648, 660, 668, 672, 680, 692, 696, 720, 768, 780, 788, 812, 864, 908, 932, 960
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OFFSET
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1,2
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COMMENT
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A111035 is the equivalent for Fibonacci numbers and has many elements in common with this sequence. T. D. Noe, who extended this sequence, noticed that, for some reason, 24 divides a lot of those n.
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FORMULA
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n such that (sum[from i=0 to n] A000032(i))/n is an integer.
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EXAMPLE
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a(1) = 1 because the first Lucas number is 2 and 2/1 = 2, an integer.
a(2) = 3 because the sum of the first three Lucas numbers is 2 + 1 + 3 = 6 and hence the average is 6/3 = 2, an integer.
a(6) = 24 because the average of the first 24 Lucas numbers is 2 + 1 + 3 + 4 + 7 + 11 + 18 + 29 + 47 + 76 + 123 + 199 + 322 + 521 + 843 + 1364 + 2207 + 3571 + 5778 + 9349 + 15127 + 24476 + 39603 + 64079) / 24 = 6990, an integer.
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MATHEMATICA
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Lucas[n_] := Fibonacci[n+1]+Fibonacci[n-1]; lst={}; s=0; Do[s=s+Lucas[n]; If[Mod[s, n]==0, AppendTo[lst, n]], {n, 1000}]; lst (Noe)
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CROSSREFS
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Cf. A000032, A111035.
Sequence in context: A099418 A108987 A035405 this_sequence A063622 A162152 A013654
Adjacent sequences: A111055 A111056 A111057 this_sequence A111059 A111060 A111061
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 07 2005
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