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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

%I #20 Feb 04 2019 07:39:05

%S 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,

%T 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,

%U 2,4,8,2,4,2,4,4,2,2,8,2,10,4,8,5,13,11,1

%N 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).

%C 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.

%H Rémy Sigrist, <a href="/A302907/a302907.png">Illustration of a(10000)</a> (using Pick's theorem)

%H Rémy Sigrist, <a href="/A302907/a302907.gp.txt">PARI program for A302907</a>

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

%e For n = 26:

%e - the 26th prime number is 101,

%e - the corresponding convex hull is as follows:

%e (1,1) +-----+ (3,1)

%e \ /

%e \ /

%e + (2,0)

%e - it has area 1, hence a(26) = 2.

%o (PARI) See Links section.

%Y Cf. A000040, A167847.

%K nonn,base

%O 1,26

%A _Rémy Sigrist_, Dec 16 2018

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