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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).
3
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
Rémy Sigrist, Illustration of a(10000) (using Pick's theorem)
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
Sequence in context: A074810 A028984 A294369 * A319561 A153181 A256624
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Dec 16 2018
STATUS
approved