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A322629 For a nonnegative 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(n).

%I A322629 #28 Aug 27 2024 18:30:35
%S A322629 1,2,3,4,5,6,7,8,9,10,1,0,1,2,3,4,5,6,7,8,3,2,1,0,1,2,3,4,5,6,5,4,3,2,
%T A322629 1,0,1,2,3,4,7,6,5,4,3,2,1,0,1,2,9,8,7,6,5,4,3,2,1,0,11,10,9,8,7,6,5,
%U A322629 4,3,2,13,12,11,10,9,8,7,6,5,4,15,14,13
%N A322629 For a nonnegative 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(n).
%C A322629 The data section starts at offset 100, however the sequence is well-defined for smaller values of n: a(n) = 0 for n = 0...99.
%H A322629 Rémy Sigrist, <a href="/A322629/b322629.txt">Table of n, a(n) for n = 100..10000</a>
%H A322629 Rémy Sigrist, <a href="/A322629/a322629.gp.txt">PARI program for A322629</a>
%F A322629 A302907(n) = a(prime(n)) where n denotes the n-th prime number.
%F A322629 a(10^n) = n-1 for any n > 0.
%F A322629 a(n) > 0 iff n belongs to A301516.
%e A322629 For n = 1212:
%e A322629 - the corresponding convex hull is as follows:
%e A322629       (2,2) +-----+ (4,2)
%e A322629            /     /
%e A322629           /     /
%e A322629    (1,1) +-----+ (3,1)
%e A322629 - it has area 2, hence a(1212) = 4.
%o A322629 (PARI) \\ See Links section.
%Y A322629 Cf. A301516, A302907.
%K A322629 nonn,base
%O A322629 100,2
%A A322629 _Rémy Sigrist_, Dec 21 2018