A395145 Maximum number of ISO A(n) sheets that fit orthogonally without overlap into a single ISO A0 sheet.

1, 2, 4, 8, 16, 32, 64, 128, 258, 516, 1038

Offset

0,2

Comments

As ISO 216 only defines A0 to A10, this sequence is complete. The values starting from n=8 deviate from powers of two (2^n) because ISO A(n) is defined in rounded whole millimeter, enabling more to fit than without rounding.

Links

Table of n, a(n) for n=0..10.

N. Friedrich, Table of how many ISO A(i) fit into a single ISO A(j) for i>=j and 0<=i,j<=10.

N. Friedrich, 1038 A10s fit into one A0, FUN 2026.

N. Friedrich, YouTube video outlining the problem and proof ideas.

Example

For n=1, two sheets of ISO A1 can be fitted into a single ISO A0.
For n=9, only 516 sheets can be fitted in, even though ~519.72 could fit in by area alone.

Crossrefs

Sequence in context: A367653 A023423 A210544 * A180210 A274861 A290666

Adjacent sequences: A395142 A395143 A395144 * A395146 A395147 A395148

Keyword

nonn,fini,full,dumb

Author

Noel Friedrich, Apr 14 2026

Status

approved