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%I #17 Aug 04 2022 05:18:01
%S 102,103,104,105,106,107,108,109,120,130,131,132,140,141,142,143,150,
%T 151,152,153,154,160,161,162,163,164,165,170,171,172,173,174,175,176,
%U 180,181,182,183,184,185,186,187,190,191,192,193,194,195
%N Acute-angled numbers with an internal digit as the vertex.
%C 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 Micah Manary, <a href="/A135601/b135601.txt">Table of n, a(n) for n = 1..2337</a>
%H Micah Manary, <a href="/A135601/a135601.py.txt">Python program</a>
%F 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 Illustration using the final term of this sequence:
%e 9 . . . . . . . . . . . . .
%e . 8 . . . . . . . . . . . 8
%e . . 7 . . . . . . . . . . .
%e . . . 6 . . . . . . . . 6 .
%e . . . . 5 . . . . . . . . .
%e . . . . . 4 . . . . . 4 . .
%e . . . . . . 3 . . . . . . .
%e . . . . . . . 2 . . 2 . . .
%e . . . . . . . . 1 . . . . .
%e . . . . . . . . . 0 . . . .
%o (Python)
%o 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 s = set()
%o for left in progressions:
%o for right in progressions:
%o dl, dr = left[1] - left[0], right[1] - right[0]
%o if dl + dr > 2:
%o if left[-1] == right[-1]: s.add(left[:-1] + right[::-1])
%o if left[0] == right[0]: s.add(left[::-1] + right[1:])
%o afull = sorted(int("".join(map(str, t))) for t in s if t[0] != 0)
%o print(afull[:53]) # _Michael S. Branicky_, Aug 02 2022
%Y Cf. A134810, A134853, A134941, A134970, A135641, A135642, A135643, A135600, A135602, A135603.
%K base,fini,nonn,full
%O 1,1
%A _Omar E. Pol_, Dec 02 2007
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