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Search: id:A101172
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| A101172 |
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Sequence whose Mobius transform leads to the first differences of the terms. |
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+0
2
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| 1, 2, 3, 5, 8, 15, 26, 51, 97, 191, 373, 745, 1472, 2943, 5859, 11708, 23365, 46729, 93349, 186697, 373200, 746372, 1492370, 2984739, 5968687, 11937366, 23873259, 47746421, 95489896, 190979791, 381953529, 763907057, 1527790748, 1527802406
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In the example, the last value in the Mobius transform of [1,2,3,5,8] is 7 and so the next term in our sequence is 8+7=15. Then, the Mobius transform of [1,2,3,5,8,15] is [1,1,2,3,7,11], which means that the next term of our sequence is 15+11=26, etc.
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EXAMPLE
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For example, the Mobius transform of the segment [1,2,3,5,8] begins [1,1,2,3], which are the first differences of these terms.
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MAPLE
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with(numtheory): F:={1}: f:=n->F[n]: g:=n->sum(mobius(divisors(n)[j])*f(n/divisors(n)[j]), j=1..tau(n)): for n from 1 to 35 do F:=F union {F[nops(F)]+g(n)} od: G:=sort(convert(F, list)); (Deutsch)
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CROSSREFS
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Sequence in context: A054539 A026702 A000047 this_sequence A006544 A110536 A049861
Adjacent sequences: A101169 A101170 A101171 this_sequence A101173 A101174 A101175
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KEYWORD
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easy,nonn
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AUTHOR
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Mark Hudson (mrmarkhudson(AT)hotmail.com), Dec 03 2004
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EXTENSIONS
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Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2005
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