A322629 For a nonnegative number m with decimal digits (d_1, ..., d_k), let s(m) be the area of the convex hull of the set of points { (i, d_i), i = 1..k }; a(n) = 2 * s(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 15, 14, 13

Offset

100,2

Comments

The data section starts at offset 100, however the sequence is well-defined for smaller values of n: a(n) = 0 for n = 0...99.

Links

Rémy Sigrist, Table of n, a(n) for n = 100..10000

Rémy Sigrist, PARI program for A322629

Formula

A302907(n) = a(prime(n)) where n denotes the n-th prime number.

a(10^n) = n-1 for any n > 0.

a(n) > 0 iff n belongs to A301516.

Example

For n = 1212:
- the corresponding convex hull is as follows:
      (2,2) +-----+ (4,2)
           /     /
          /     /
   (1,1) +-----+ (3,1)
- it has area 2, hence a(1212) = 4.

Prog

(PARI) See Links section.

Crossrefs

Cf. A301516, A302907.

Sequence in context: A320486 A321801 A278946 * A190599 A214587 A365762

Adjacent sequences: A322626 A322627 A322628 * A322630 A322631 A322632

Keyword

nonn,base

Author

Rémy Sigrist, Dec 21 2018

Status

approved