A395536 Decimal expansion of the sum of the reciprocals of pentagonal polygorials A084939.

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, 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, 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

Offset

1,1

Links

Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Formula

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.

Example

2.2174463179875775270548915352217019990458226207124421588256580269...

Mathematica

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 *)

Crossrefs

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

Cf. A084939.

Sequence in context: A021455 A271460 A248924 * A380421 A307455 A136502

Adjacent sequences: A395533 A395534 A395535 * A395537 A395538 A395539

Keyword

nonn,cons

Author

Kelvin Voskuijl, Apr 27 2026

Status

approved