A135603 Obtuse-angled numbers with an internal digit as the vertex.

100, 110, 112, 113, 114, 115, 116, 117, 118, 119, 122, 124, 125, 126, 127, 128, 129, 133, 134, 136, 137, 138, 139, 144, 145, 146, 148, 149, 155, 156, 157, 158, 166, 167, 168, 169, 177, 178, 179, 188, 189, 199, 200, 211, 220, 221, 223, 224, 225, 226, 227, 228, 229, 233

Offset

1,1

Comments

The structure of digits represents an obtuse angle. The vertex is an internal digit. In the graphic representation the points are connected by imaginary line segments from left to right.

For each k >= 11, there are 354 k-digit terms. - Michael S. Branicky, Aug 03 2022

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10232

Example

Illustration of the number 9753111:
  9 . . . . . .
  . . . . . . .
  . 7 . . . . .
  . . . . . . .
  . . 5 . . . .
  . . . . . . .
  . . . 3 . . .
  . . . . . . .
  . . . . 1 1 1
  . . . . . . .

Prog

(Python)
from itertools import count, islice
def ok3(n):
    if n < 100: return False
    d = list(map(int, str(n)))
    m1, m2 = (d[1]-d[0], d[-1]-d[-2])
    return len({m1, m2}) == 2 and m1*m2 >= 0
def agen():
    seeds = [k for k in range(100, 1000) if ok3(k)]
    for digits in count(4):
        yield from sorted(seeds)
        new, pow10 = set(), 10**(digits-1)
        for q in seeds:
            d = list(map(int, str(q)))
            e1, e2 = d[0] - (d[1]-d[0]), d[-1] + (d[-1]-d[-2])
            if 9 >= e1 > 0: new.add(e1*pow10 + q)
            if 9 >= e2 >= 0: new.add(10*q + e2)
        seeds = new
print(list(islice(agen(), 54))) # Michael S. Branicky, Aug 03 2022

Crossrefs

Cf. A134810, A134853, A134941, A134970, A135641, A135642, A135643, A135600, A135601, A135602.

Sequence in context: A134496 A191752 A165406 * A044866 A290948 A033828

Adjacent sequences: A135600 A135601 A135602 * A135604 A135605 A135606

Keyword

base,nonn

Author

Omar E. Pol, Dec 02 2007

Extensions

a(49) and beyond from Michael S. Branicky, Aug 03 2022

Status

approved