cp's OEIS Frontend

A135601 Acute-angled numbers with an internal digit as the vertex.

%I A135601 #17 Aug 04 2022 05:18:01
%S A135601 102,103,104,105,106,107,108,109,120,130,131,132,140,141,142,143,150,
%T A135601 151,152,153,154,160,161,162,163,164,165,170,171,172,173,174,175,176,
%U A135601 180,181,182,183,184,185,186,187,190,191,192,193,194,195
%N A135601 Acute-angled numbers with an internal digit as the vertex.
%C A135601 The structure of digits represents an acute 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 14 digits: 98765432102468.
%H A135601 Micah Manary, <a href="/A135601/b135601.txt">Table of n, a(n) for n = 1..2337</a>
%H A135601 Micah Manary, <a href="/A135601/a135601.py.txt">Python program</a>
%F A135601 If a(n) does not end in 0, then A004086(a(n)) is a term; if a(n) does not start with 9, then A061601(a(n)) is a term. - _Michael S. Branicky_, Aug 02 2022
%e A135601 Illustration using the final term of this sequence:
%e A135601   9 . . . . . . . . . . . . .
%e A135601   . 8 . . . . . . . . . . . 8
%e A135601   . . 7 . . . . . . . . . . .
%e A135601   . . . 6 . . . . . . . . 6 .
%e A135601   . . . . 5 . . . . . . . . .
%e A135601   . . . . . 4 . . . . . 4 . .
%e A135601   . . . . . . 3 . . . . . . .
%e A135601   . . . . . . . 2 . . 2 . . .
%e A135601   . . . . . . . . 1 . . . . .
%e A135601   . . . . . . . . . 0 . . . .
%o A135601 (Python)
%o A135601 progressions = set(tuple(range(i, j+1, d)) for i in range(10) for d in range(1, 10-i) for j in range(i+d, 10))
%o A135601 s = set()
%o A135601 for left in progressions:
%o A135601     for right in progressions:
%o A135601         dl, dr = left[1] - left[0], right[1] - right[0]
%o A135601         if dl + dr > 2:
%o A135601             if left[-1] == right[-1]: s.add(left[:-1] + right[::-1])
%o A135601             if left[0] == right[0]: s.add(left[::-1] + right[1:])
%o A135601 afull = sorted(int("".join(map(str, t))) for t in s if t[0] != 0)
%o A135601 print(afull[:53]) # _Michael S. Branicky_, Aug 02 2022
%Y A135601 Cf. A134810, A134853, A134941, A134970, A135641, A135642, A135643, A135600, A135602, A135603.
%K A135601 base,fini,nonn,full
%O A135601 1,1
%A A135601 _Omar E. Pol_, Dec 02 2007