A347345 Decimal expansion of 1 / 1^1 + 1 / (1^1 * 2^2) + 1 / (1^1 * 2^2 * 3^3) + 1 / (1^1 * 2^2 * 3^3 * 4^4) + ...

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

Offset

1,2

Comments

This constant is irrational (Stucky, 2016). - Amiram Eldar, Apr 30 2023

Links

Table of n, a(n) for n=1..115.

Joshua Stucky, Several Theorems Concerning the Irrationality of Certain Infinite Series Involving Tetrations, The Pentagon, Vol. 75, No. 2 (2016), pp. 4-9.

Eric Weisstein's World of Mathematics, Hyperfactorial.

Example

1.2592954398150628876913596498837350926311457518421...

Mathematica

With[{m = 105}, RealDigits[N[Sum[1/Hyperfactorial[n], {n, 1, Infinity}], m + 2], 10, m][[1]]] (* Amiram Eldar, Apr 30 2023 *)
RealDigits[Total[Table[1/Times@@(Range[n]^Range[n]), {n, 30}]], 10, 120][[1]] (* Harvey P. Dale, Oct 07 2023 *)

Crossrefs

Cf. A000312, A002109, A073009, A083648, A091131, A137986, A287013, A347352.

Sequence in context: A019802 A248934 A011432 * A324835 A082183 A332554

Adjacent sequences: A347342 A347343 A347344 * A347346 A347347 A347348

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Aug 28 2021

Status

approved