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

1,1

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

Prog

(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

Crossrefs

Cf. A134999, A135643, A302907.

Sequence in context: A000865 A135600 A134999 * A204581 A135641 A330859

Adjacent sequences: A301513 A301514 A301515 * A301517 A301518 A301519

Keyword

nonn,base

Author

Rémy Sigrist, Dec 16 2018

Status

approved