A291719 Numbers occurring in Ezra Ehrenkrantz's "Modular Coordination System".

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 128, 144, 180, 192, 216, 240, 288, 360, 384, 432, 576, 720, 1152

Offset

1,2

Comments

Cited from Jay Kapraff’s article: "... architect Ezra Ehrenkrantz created a system of architectural proportion that incorporates aspects of Alberti’s and Palladio’s systems made up of lengths factorable by the primes 2, 3, and 5, along with the additive properties of Fibonacci series."

References

Ezra Ehrenkrantz, Modular Number Pattern, Tiranti, London 1956.

Links

Table of n, a(n) for n=1..44.

Jay Kappraff, Musical Proportions at the Basis of Systems of Architectural Proportion both Ancient and Modern, Chapter 37 in Volume I of K. Williams and M.J. Ostwald (eds.), Architecture and Mathematics from Antiquity to the Future, DOI 10.1007/978-3-319-00137-1_37, Springer International Publishing Switzerland 2015

Formula

Numbers of the form Fibonacci(i+2)*2^j*3^k; i, j=0..4, k=0..2.

Example

The number pattern in three dimensions:
                     A    B     C     D     E
          Plate 3 +---+-----+-----+-----+-----+
                 /|  9   18    36    72   144 |
                / | 18   36    72   144   288 |
               /  | 27   54   108   216   432 |
              /   | 45   90   180   360   720 |
             /    | 72  144   288   576  1152 |
            /     +---+-----+-----+-----+-----+
           / A    B     C     D     E        /
  Plate 2 /---+-----+-----+-----+-----+     /
         /|  3    6    12    24    48 |    /
        / |  6   12    24    48    96 |   /
       /  |  9   18    36    72   144 |  /
      /   | 15   30    60   120   240 | /
     /    | 24   48    96   192   384 |/
    /     +---+-----+-----+-----+-----/
   /  A    B     C     D     E       /
  +---+-----+-----+-----+-----+ Plate 1
  |  1    2     4     8    16 |    /
  |  2    4     8    16    32 |   /
  |  3    6    12    24    48 |  /
  |  5   10    20    40    80 | /
  |  8   16    32    64   128 |/
  +---+-----+-----+-----+-----+

Maple

with(combinat):
{seq(seq(seq(fibonacci(i+2)*2^j*3^k, k=0..2), j=0..4), i=0..4)}[]; # Alois P. Heinz, Aug 30 2017

Crossrefs

Cf. A000045, A051037.

Sequence in context: A257997 A070023 A035303 * A360425 A018609 A243390

Adjacent sequences: A291716 A291717 A291718 * A291720 A291721 A291722

Keyword

nonn,fini,full

Author

Hugo Pfoertner, Aug 30 2017

Status

approved