cp's OEIS Frontend

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

%I A135603 #12 Aug 03 2022 18:29:33
%S A135603 100,110,112,113,114,115,116,117,118,119,122,124,125,126,127,128,129,
%T A135603 133,134,136,137,138,139,144,145,146,148,149,155,156,157,158,166,167,
%U A135603 168,169,177,178,179,188,189,199,200,211,220,221,223,224,225,226,227,228,229,233
%N A135603 Obtuse-angled numbers with an internal digit as the vertex.
%C A135603 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.
%C A135603 For each k >= 11, there are 354 k-digit terms. - _Michael S. Branicky_, Aug 03 2022
%H A135603 Michael S. Branicky, <a href="/A135603/b135603.txt">Table of n, a(n) for n = 1..10232</a>
%e A135603 Illustration of the number 9753111:
%e A135603   9 . . . . . .
%e A135603   . . . . . . .
%e A135603   . 7 . . . . .
%e A135603   . . . . . . .
%e A135603   . . 5 . . . .
%e A135603   . . . . . . .
%e A135603   . . . 3 . . .
%e A135603   . . . . . . .
%e A135603   . . . . 1 1 1
%e A135603   . . . . . . .
%o A135603 (Python)
%o A135603 from itertools import count, islice
%o A135603 def ok3(n):
%o A135603     if n < 100: return False
%o A135603     d = list(map(int, str(n)))
%o A135603     m1, m2 = (d[1]-d[0], d[-1]-d[-2])
%o A135603     return len({m1, m2}) == 2 and m1*m2 >= 0
%o A135603 def agen():
%o A135603     seeds = [k for k in range(100, 1000) if ok3(k)]
%o A135603     for digits in count(4):
%o A135603         yield from sorted(seeds)
%o A135603         new, pow10 = set(), 10**(digits-1)
%o A135603         for q in seeds:
%o A135603             d = list(map(int, str(q)))
%o A135603             e1, e2 = d[0] - (d[1]-d[0]), d[-1] + (d[-1]-d[-2])
%o A135603             if 9 >= e1 > 0: new.add(e1*pow10 + q)
%o A135603             if 9 >= e2 >= 0: new.add(10*q + e2)
%o A135603         seeds = new
%o A135603 print(list(islice(agen(), 54))) # _Michael S. Branicky_, Aug 03 2022
%Y A135603 Cf. A134810, A134853, A134941, A134970, A135641, A135642, A135643, A135600, A135601, A135602.
%K A135603 base,nonn
%O A135603 1,1
%A A135603 _Omar E. Pol_, Dec 02 2007
%E A135603 a(49) and beyond from _Michael S. Branicky_, Aug 03 2022