A179393 Period of the Fibonacci-type sequence described by A015134.

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

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: A355828 A091839 A155789 * A347954 A217598 A347235

Adjacent sequences: A179390 A179391 A179392 * A179394 A179395 A179396

Keyword

nonn,tabf

Author

Will Nicholes, Jul 12 2010

Status

approved