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

1,26

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.

Links

Table of n, a(n) for n=1..82.

Rémy Sigrist, Illustration of a(10000) (using Pick's theorem)

Rémy Sigrist, PARI program for A302907

Formula

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000040, A167847.

Sequence in context: A074810 A028984 A294369 * A319561 A153181 A256624

Adjacent sequences: A302904 A302905 A302906 * A302908 A302909 A302910

Keyword

nonn,base

Author

Rémy Sigrist, Dec 16 2018

Status

approved