A395536 - OEIS

%I #11 May 03 2026 00:06:23

%S 2,2,1,7,4,4,6,3,1,7,9,8,7,5,7,7,5,2,7,0,5,4,8,9,1,5,3,5,2,2,1,7,0,1,

%T 9,9,9,0,4,5,8,2,2,6,2,0,7,1,2,4,4,2,1,5,8,8,2,5,6,5,8,0,2,6,9,0,9,3,

%U 1,7,7,5,1,6,8,4,7,2,7,8,6,1,6,2,1,0,5,8,6,4,0,4,5,7,9,2,6,6,6,7,4,8,3,2,3,8,0,9,1,0,2

%N Decimal expansion of the sum of the reciprocals of pentagonal polygorials A084939.

%H Kelvin Voskuijl, <a href="/A395536/b395536.txt">Table of n, a(n) for n = 1..20000</a>

%F Equals (3^(1/6)/2) * Gamma(2/3) * (sqrt(3) * AiryAi(6^(1/3)) + AiryBi(6^(1/3))), where AiryAi and AiryBi are the Airy functions of the first and second kind, respectively.

%e 2.2174463179875775270548915352217019990458226207124421588256580269...

%t RealDigits[(3^(1/6)/2) * Gamma[2/3] * (Sqrt[3]*AiryAi[6^(1/3)] + AiryBi[6^(1/3)]), 10, 120][[1]] (* _Amiram Eldar_, Apr 28 2026 *)

%Y Cf. A001113 (of factorials), A070910 (of factorials squared), A395537-A395538 (hexagonal and heptagonal).

%Y Cf. A084939.

%K nonn,cons

%O 1,1

%A _Kelvin Voskuijl_, Apr 27 2026