A036286 Periodic vertical binary vectors of Fibonacci numbers, topmost bits being most significant.

3, 6, 90, 202474, 802914372650, 124876754670311211270396330, 2261740218128437766312179308277308483058208661638110890, 7527129205899945471753233641719262207829849606092782843679109711117799287001392666047916596823438974998183293610

Offset

0,1

Links

A. Karttunen, Table of n, a(n) for n = 0..10

A. Karttunen, C program for computing this sequence

Formula

a(n) = Sum_{k=0..A007283(n)-1} ([A000045((A007283(n)-1)-k)/(2^n)] mod 2) * 2^k, where [] stands for floor function.

Example

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 n-th 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.

Crossrefs

See comments at A036284. a(n)/A036287(n) can be interpreted as fractions.

Sequence in context: A363410 A211896 A299433 * A084008 A092680 A101574

Adjacent sequences: A036283 A036284 A036285 * A036287 A036288 A036289

Keyword

nonn,base

Author

Antti Karttunen, Nov 01 1998. Entry revised Dec 29 2007.

Status

approved