A135603 - OEIS

%I #12 Aug 03 2022 18:29:33

%S 100,110,112,113,114,115,116,117,118,119,122,124,125,126,127,128,129,

%T 133,134,136,137,138,139,144,145,146,148,149,155,156,157,158,166,167,

%U 168,169,177,178,179,188,189,199,200,211,220,221,223,224,225,226,227,228,229,233

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

%C 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 For each k >= 11, there are 354 k-digit terms. - _Michael S. Branicky_, Aug 03 2022

%H Michael S. Branicky, <a href="/A135603/b135603.txt">Table of n, a(n) for n = 1..10232</a>

%e Illustration of the number 9753111:

%e   9 . . . . . .

%e   . . . . . . .

%e   . 7 . . . . .

%e   . . . . . . .

%e   . . 5 . . . .

%e   . . . . . . .

%e   . . . 3 . . .

%e   . . . . . . .

%e   . . . . 1 1 1

%e   . . . . . . .

%o (Python)

%o from itertools import count, islice

%o def ok3(n):

%o     if n < 100: return False

%o     d = list(map(int, str(n)))

%o     m1, m2 = (d[1]-d[0], d[-1]-d[-2])

%o     return len({m1, m2}) == 2 and m1*m2 >= 0

%o def agen():

%o     seeds = [k for k in range(100, 1000) if ok3(k)]

%o     for digits in count(4):

%o         yield from sorted(seeds)

%o         new, pow10 = set(), 10**(digits-1)

%o         for q in seeds:

%o             d = list(map(int, str(q)))

%o             e1, e2 = d[0] - (d[1]-d[0]), d[-1] + (d[-1]-d[-2])

%o             if 9 >= e1 > 0: new.add(e1*pow10 + q)

%o             if 9 >= e2 >= 0: new.add(10*q + e2)

%o         seeds = new

%o print(list(islice(agen(), 54))) # _Michael S. Branicky_, Aug 03 2022

%Y Cf. A134810, A134853, A134941, A134970, A135641, A135642, A135643, A135600, A135601, A135602.

%K base,nonn

%O 1,1

%A _Omar E. Pol_, Dec 02 2007

%E a(49) and beyond from _Michael S. Branicky_, Aug 03 2022