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A179393 Period of the Fibonacci-type sequence described by A015134. 3
1, 1, 3, 1, 8, 1, 6, 3, 6, 1, 20, 4, 1, 24, 8, 3, 1, 16, 16, 16, 1, 12, 6, 12, 3, 6, 12, 12, 1, 24, 24, 8, 24, 1, 60, 20, 3, 12, 4, 1, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 5, 10, 5, 1, 24, 24, 6, 8, 3, 24, 6, 24, 24, 1, 28, 28, 28, 28, 28, 28, 1, 48, 16, 48, 16, 48, 16, 3, 1, 40, 40, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

First terms of A015134 are 1, 2, 2 and 4, meaning that there are 1, 2, 2 and 4 Fibonacci-type sequences modulo 1, 2, 3 and 4 respectively. These are:

mod 1: 0

mod 2: 0

mod 2: 0,1,1

mod 3: 0

mod 3: 0,1,1,2,0,2,2,1

mod 4: 0

mod 4: 0,1,1,2,3,1

mod 4: 0,2,2

mod 4: 0,3,3,2,1,3

The first sequence for each modulus is the period-1 sequence of 0,0,0... This has the helpful side effect of causing 1 to act as a delimiter between modulus entries: the first 1 indicates the start of modulo-1 sequences, the second 1 indicates the start of modulo-2 sequences, etc.

For each group of sequences (the group start indicated by a 1), the sum of the periods in that group equal the square of the modulus. 1 = 1, (1+3) = 4, (1+8) = 9, (1+6+3+6) = 16, etc.

LINKS

Table of n, a(n) for n=1..82.

Will Nicholes, Fibonacci numbers and Pisano periods.

CROSSREFS

Cf. A015134, A179390, A179391, A179392.

Sequence in context: A059526 A091839 A155789 * A217598 A280207 A182510

Adjacent sequences:  A179390 A179391 A179392 * A179394 A179395 A179396

KEYWORD

nonn,tabf

AUTHOR

Will Nicholes, Jul 12 2010

STATUS

approved

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Last modified September 24 04:27 EDT 2017. Contains 292403 sequences.