A370353 Decimal expansion of the average number of rolls of a fair standard dice until the total sum of all rolls is a prime number.

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

Offset

1,1

Comments

The data was calculated by Martinez and Zeilberger (2023).

Links

Table of n, a(n) for n=1..104.

Noga Alon and Yaakov Malinovsky, Hitting a prime in 2.43 dice rolls (on average), The American Statistician, Vol. 77, No. 3 (2023), pp. 301-303; arXiv preprint, arXiv:2209.07698 [math.PR], 2022-2023.

Shane Chern, Hitting a prime by rolling a die with infinitely many faces, The American Statistician (2024); arXiv preprint, arXiv:2306.14073 [math.NT], 2023.

Anirban DasGupta, Student Puzzle Corner 17 (and solution to SPC16), IMS Bulletin, Vol. 46, No. 2 (2017), p. 7; entire issue.

Anirban DasGupta, Student Puzzle Corner 18 (and solution to Puzzle 17), IMS Bulletin, Vol. 46, No. 5 (2017), p. 9; entire issue.

Yaakov Malinovsky and Noga Alon, Hitting a prime in 2.43 dice rolls (on average), Rutgers Experimental Mathematics Seminar, November 17, 2022.

Lucy Martinez and Doron Zeilberger, How many Dice Rolls Would It Take to Reach Your Favorite Kind of Number?, Maple Transactions, Vol. 3, No. 3 (2023), Article 15953; arXiv preprint, arXiv:2302.00143 [math.CO], 2023.

Doron Zeilberger, How many Dice Rolls Would It Take to Reach Your Favorite Kind of Number?, Maple packages, 2023.

Example

2.428497913693504230361652177658421796651200211185346...

Crossrefs

Cf. A096256.

Sequence in context: A278531 A366279 A364297 * A095728 A279354 A278220

Adjacent sequences: A370350 A370351 A370352 * A370354 A370355 A370356

Keyword

nonn,cons

Author

Amiram Eldar, Feb 16 2024

Status

approved