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

Author

Omar E. Pol, Dec 02 2007

Keywords

• base
• fini
• full
• nonn

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.

Examples

			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 . . . . . . . . .
		

Links

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

Crossrefs

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

Programs

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