A362199 Decimal expansion of the sum of the reciprocals of the Busy Beaver numbers (A060843).

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

Offset: 1

Author

Robert C. Lyons, Apr 10 2023

Keywords

• nonn
• cons
• hard

Comments

Equal to 1/BB(1) + 1/BB(2) + 1/BB(3) + ... = 1/A060843(1) + 1/A060843(2) + 1/A060843(3) + ...

A homework assignment in Scott Aaronson's "PHYS771 Lecture 3: Gödel, Turing, and Friends" (see links) asks if 1/BB(1) + 1/BB(2) + 1/BB(3) + ... is a computable real number. Scott Aaronson's "PHYS771 Lecture 4: Minds and Machines" (see links), which provides the answers to the homework assignment, proves that the number is not computable.

Because BB(5) was proved to be 47176870 (see here https://discuss.bbchallenge.org/t/july-2nd-2024-we-have-proved-bb-5-47-176-870/237) and BB(6) was proved to be greater than 10^^15 (see here https://www.sligocki.com/2022/06/21/bb-6-2-t15.html), over 10^14 terms are known. - Matthew Schulz, Dec 13 2024.

Examples

			1.22363152987506567206776268317631246216226466...
		

Links

• Matthew Schulz, Table of n, a(n) for n = 1..20000
• Scott Aaronson, PHYS771 Lecture 3: Gödel, Turing, and Friends.
• Scott Aaronson, PHYS771 Lecture 4: Minds and Machines.

Crossrefs

Cf. A060843.

Formula

1/A060843(1) + 1/A060843(2) + 1/A060843(3) + ...

Extensions

a(8) onwards from Matthew Schulz, Dec 13 2024