

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).


1



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, 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, 4, 3, 2, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 15, 14, 13
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

100,2


COMMENTS

The data section starts at offset 100, however the sequence is welldefined for smaller values of n: a(n) = 0 for n = 0...99.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 100..10000
Rémy Sigrist, PARI program for A322629


FORMULA

A302907(n) = a(prime(n)) where n denotes the nth prime number.
a(10^n) = n1 for any n > 0.
a(n) > 0 iff n belongs to A301516.


EXAMPLE

For n = 1212:
 the corresponding convex hull is as follows:
(2,2) ++ (4,2)
/ /
/ /
(1,1) ++ (3,1)
 it has area 2, hence a(1212) = 4.


PROG

(PARI) See Links section.


CROSSREFS

Cf. A301516, A302907.
Sequence in context: A320486 A321801 A278946 * A190599 A214587 A010889
Adjacent sequences: A322626 A322627 A322628 * A322630 A322631 A322632


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Dec 21 2018


STATUS

approved



