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Search: id:A036286
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| A036286 |
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Periodic vertical binary vectors of Fibonacci numbers, topmost bits being most significant. |
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+0
3
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| 3, 6, 90, 202474, 802914372650, 124876754670311211270396330, 2261740218128437766312179308277308483058208661638110890, 7527129205899945471753233641719262207829849606092782843679109711117799287001392666047916596823438974998183293610
(list; graph; listen)
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OFFSET
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0,1
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..10
A. Karttunen, C program for computing this sequence
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FORMULA
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a(n) = Sum_{k=0..A007283(n)-1} ([A000045((A007283(n)-1)-k)/(2^n)] mod 2) * 2^k, where [] stands for floor function.
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EXAMPLE
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When Fibonacci numbers are written in binary (see A004685), under each other as:
0000000 (0)
0000001 (1)
0000001 (1)
0000010 (2)
0000011 (3)
0000101 (5)
0001000 (8)
0001101 (13)
0010101 (21)
0100010 (34)
0110111 (55)
1011001 (89)
it can be seen that the bits in the nth column from right repeat after the period of A007283(n): 3, 6, 12, 24, ... (See also A001175). This sequence is formed from those bits: 011, binary for 3, thus a(0) = 3. 000110, binary for 6, thus a(1) = 6, 000001011010, binary for 90, thus a(2) = 90. Cf. A036284.
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CROSSREFS
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See comments at A036284. a(n)/A036287(n) can be interpreted as fractions.
Sequence in context: A050722 A069502 A023174 this_sequence A084008 A092680 A101574
Adjacent sequences: A036283 A036284 A036285 this_sequence A036287 A036288 A036289
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KEYWORD
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nonn,base
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AUTHOR
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Antti Karttunen (His_Firstname.His_Surname(AT)gmail.com), Nov 01 1998. Entry revised Dec 29 2007.
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