A135602 Right-angled numbers with an internal digit as the vertex.

101, 121, 212, 232, 323, 343, 434, 454, 545, 565, 656, 676, 767, 787, 878, 898, 989, 1012, 1210, 1232, 2101, 2123, 2321, 2343, 3212, 3234, 3432, 3454, 4323, 4345, 4543, 4565, 5434, 5456, 5654, 5676, 6545, 6567, 6765, 6787, 7656, 7678, 7876, 7898, 8767, 8789, 8987

Offset

1,1

Comments

The structure of digits represents a right angle. The vertex is an internal digit. In the graphic representation the points are connected by imaginary line segments from left to right. This sequence is finite. The final term has 19 digits: 9876543210123456789.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..525

Example

Illustration using the final term of this sequence:
  9 . . . . . . . . . . . . . . . . . 9
  . 8 . . . . . . . . . . . . . . . 8 .
  . . 7 . . . . . . . . . . . . . 7 . .
  . . . 6 . . . . . . . . . . . 6 . . .
  . . . . 5 . . . . . . . . . 5 . . . .
  . . . . . 4 . . . . . . . 4 . . . . .
  . . . . . . 3 . . . . . 3 . . . . . .
  . . . . . . . 2 . . . 2 . . . . . . .
  . . . . . . . . 1 . 1 . . . . . . . .
  . . . . . . . . . 0 . . . . . . . . .

Prog

(Python)
ups = list(tuple(range(i, j)) for i in range(9) for j in range(i+2, 11))
s = set(L[::-1] + R[1:] for L in ups for R in ups if L[0] == R[0])
s |= set(L[:-1] + R[::-1] for L in ups for R in ups if L[-1] == R[-1])
afull = sorted(int("".join(map(str, t))) for t in s if t[0] != 0)
print(afull[:47]) # Michael S. Branicky, Aug 02 2022

Crossrefs

Cf. A134810, A134853, A134941, A134970, A135641, A135642, A135643, A135600, A135601, A135603.

Sequence in context: A046075 A088882 A261453 * A095635 A060916 A075793

Adjacent sequences: A135599 A135600 A135601 * A135603 A135604 A135605

Keyword

base,fini,full,nonn

Author

Omar E. Pol, Dec 02 2007

Status

approved