A301516 Numbers n with decimal expansion (d_1, ..., d_k) such that the convex hull of the set of points { (i, d_i), i = 1..k } has positive area.

100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 154, 155

Offset: 1

Author

Rémy Sigrist, Dec 16 2018

Keywords

• nonn
• base

Comments

This sequence is the complement of the straight-line numbers (0..99 alongside A135643).

This sequence first differs from A134999 at n = 857: a(857) = 1001 whereas A134999(857) = 1011.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A134999, A135643, A302907.

Programs

PARI

is(n, base=10) = my (d=digits(n, base)); for (i=1, #d-2, if (d[i]+d[i+2]-2*d[i+1], return (1))); return (0)

Python

def ok(n):
    d = list(map(int, str(n)))
    return any(d[i]+d[i+2]-2*d[i+1] != 0 for i in range(len(d)-2))
print([k for k in range(1002) if ok(k)]) # Michael S. Branicky, Aug 03 2022 after Rémy Sigrist