A302907 For any 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(prime(n)) (where prime(n) denotes the n-th prime number).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 8, 10, 2, 4, 4, 2, 4, 2, 8, 2, 8, 4, 10, 4, 14, 16, 14, 10, 8, 1, 1, 5, 7, 1, 5, 5, 7, 1, 7, 1, 11, 5, 13, 11, 13, 10, 2, 4, 8, 2, 4, 2, 4, 4, 2, 2, 8, 2, 10, 4, 8, 5, 13, 11, 1

Offset: 1

Author

Rémy Sigrist, Dec 16 2018

Keywords

• nonn
• base

Comments

As in A167847 and in similar sequences, we map the digits of a number to a set of points and consider its graphical and geometrical properties.

Examples

			For n = 26:
- the 26th prime number is 101,
- the corresponding convex hull is as follows:
   (1,1) +-----+ (3,1)
          \   /
           \ /
            + (2,0)
- it has area 1, hence a(26) = 2.
		

Links

• Rémy Sigrist, Illustration of a(10000) (using Pick's theorem)
• Rémy Sigrist, PARI program for A302907

Crossrefs

Cf. A000040, A167847.

Programs

PARI

See Links section.

Formula

a(n) = 0 iff the n-th prime number belongs to A167847.