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

Author

Will Nicholes, Jul 12 2010

Keywords

• nonn
• tabf

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

• Will Nicholes, Fibonacci numbers and Pisano periods.

Crossrefs

Cf. A015134, A179390, A179391, A179392.