A093613 Table read by rows: row n is the n-th Primary Phyllotaxis Sequence (PPS), which has F(n+1) terms, where F(n) is the n-th Fibonacci number. For 1 <= k < F(n+1), a(n, k) = -k*F(n-1) mod F(n+1). a(n, F(n+1)) = F(n+1).

1, 1, 2, 2, 1, 3, 3, 1, 4, 2, 5, 5, 2, 7, 4, 1, 6, 3, 8, 8, 3, 11, 6, 1, 9, 4, 12, 7, 2, 10, 5, 13, 13, 5, 18, 10, 2, 15, 7, 20, 12, 4, 17, 9, 1, 14, 6, 19, 11, 3, 16, 8, 21, 21, 8, 29, 16, 3, 24, 11, 32, 19, 6, 27, 14, 1, 22, 9, 30, 17, 4, 25, 12, 33, 20, 7, 28, 15, 2, 23, 10, 31, 18, 5, 26

Offset

1,3

Comments

Related to the arrangement of stalks or florets on a plant.

In the reference, the rows of the table appear as rings of the Primary Phyllotaxis Wheel, alternating clockwise and counterclockwise.

References

Jay Kappraff, "Beyond Measure, A Guided Tour Through Nature, Myth and Number", World Scientific, 2002, p. 522-538., (p. 535, Adamson's Primary Phyllotaxis Wheel).

Links

Table of n, a(n) for n=1..85.

Jay Kappraff, Growth in Plants: A Study in Number

Example

The row of 13 terms starts with 8. Successive terms are obtained by subtracting 5 or adding 8: 8, 3, 11, 6, 1, 9, 4, 12, 7, 2, 10, 5, 13.

Crossrefs

Sequence in context: A264263 A291123 A292594 * A344086 A335933 A344087

Adjacent sequences: A093610 A093611 A093612 * A093614 A093615 A093616

Keyword

nonn,easy,tabf

Author

Gary W. Adamson, Apr 04 2004

Extensions

Edited by David Wasserman, Oct 26 2006

Status

approved