cp's OEIS Frontend

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).

%I A302907 #20 Feb 04 2019 07:39:05
%S A302907 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 A302907 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 A302907 2,4,8,2,4,2,4,4,2,2,8,2,10,4,8,5,13,11,1
%N 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).
%C A302907 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 A302907 Rémy Sigrist, <a href="/A302907/a302907.png">Illustration of a(10000)</a> (using Pick's theorem)
%H A302907 Rémy Sigrist, <a href="/A302907/a302907.gp.txt">PARI program for A302907</a>
%F A302907 a(n) = 0 iff the n-th prime number belongs to A167847.
%e A302907 For n = 26:
%e A302907 - the 26th prime number is 101,
%e A302907 - the corresponding convex hull is as follows:
%e A302907    (1,1) +-----+ (3,1)
%e A302907           \   /
%e A302907            \ /
%e A302907             + (2,0)
%e A302907 - it has area 1, hence a(26) = 2.
%o A302907 (PARI) See Links section.
%Y A302907 Cf. A000040, A167847.
%K A302907 nonn,base
%O A302907 1,26
%A A302907 _Rémy Sigrist_, Dec 16 2018