A322629 - OEIS

%I #28 Aug 27 2024 18:30:35

%S 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 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 4,3,2,13,12,11,10,9,8,7,6,5,4,15,14,13

%N 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 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 Rémy Sigrist, <a href="/A322629/b322629.txt">Table of n, a(n) for n = 100..10000</a>

%H Rémy Sigrist, <a href="/A322629/a322629.gp.txt">PARI program for A322629</a>

%F A302907(n) = a(prime(n)) where n denotes the n-th prime number.

%F a(10^n) = n-1 for any n > 0.

%F a(n) > 0 iff n belongs to A301516.

%e For n = 1212:

%e - the corresponding convex hull is as follows:

%e       (2,2) +-----+ (4,2)

%e            /     /

%e           /     /

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

%e - it has area 2, hence a(1212) = 4.

%o (PARI) \\ See Links section.

%Y Cf. A301516, A302907.

%K nonn,base

%O 100,2

%A _Rémy Sigrist_, Dec 21 2018