# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a195398 Showing 1-1 of 1 %I A195398 #7 Jul 18 2021 05:44:43 %S A195398 6,0,1,1,2,6,3,9,6,9,1,7,6,5,3,2,5,1,6,5,4,1,2,6,3,7,8,7,7,7,2,6,1,0, %T A195398 8,0,6,6,8,6,4,0,3,9,9,9,2,3,8,7,2,4,8,9,7,2,4,2,0,2,9,3,6,6,1,0,0,0, %U A195398 5,1,7,6,6,5,0,8,6,4,9,9,1,2,4,1,5,6,1,6,4,8,7,5,9,2,4,6,1,9,2,3,6,8,9 %N A195398 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(3),sqrt(5),sqrt(8) right triangle ABC. %C A195398 See A195284 for definitions and a general discussion. %e A195398 Philo(ABC,I)=0.6011263969176532516541263787772610806686403999... %t A195398 a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8]; %t A195398 f = 2 a*b/(a + b + c); %t A195398 x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ] %t A195398 x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ] %t A195398 x3 = f*Sqrt[2] %t A195398 N[x1, 100] %t A195398 RealDigits[%] (* (A) A195395 *) %t A195398 N[x2, 100] %t A195398 RealDigits[%] (* (B) A195396 *) %t A195398 N[x3, 100] %t A195398 RealDigits[%] (* (C) A195397 *) %t A195398 N[(x1 + x2 + x3)/(a + b + c), 100] %t A195398 RealDigits[%] (* Philo(ABC,I) A195398 *) %Y A195398 Cf. A195284. %K A195398 nonn,cons %O A195398 0,1 %A A195398 _Clark Kimberling_, Sep 17 2011 %E A195398 a(99) corrected by _Georg Fischer_, Jul 18 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE