A385333 The numbers of people such that, in the variant of the Josephus problem in which three people are skipped and then one is eliminated, the last person is the last to be eliminated.

1, 21, 38, 51, 122, 163, 689, 919, 2906, 3875, 5167, 51617, 68823, 163137, 290022, 1629537, 6866858, 9155811, 16276998, 28936886, 38582515, 121939802, 162586403, 216781871, 289042495, 513853325, 685137767, 913517023, 2165373685, 12166489185, 38452113969, 121527668842

Offset: 1

Author

Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Jun 25 2025

Keywords

• nonn

Comments

This sequence can be used in magic tricks with under-under-under-down dealing pattern. The deck sizes in this sequence guarantee that after the dealing, the last card dealt is the one that was initially on the bottom.

Examples

			Suppose there are 5 people in a circle. After three people are skipped, the person number 4 is eliminated. The leftover people are 5,1,2,3 in order. Then person number 3 eliminated, and the leftover people are 5,1,2 in order. Then person number 5 is eliminated, and the leftover people are 1,2 in order. Then person number 2 is eliminated, and person 1 is freed. Thus, 5 is NOT in this sequence.
		

Crossrefs

Cf. A088333, A384770, A384772, A384774, A385327.

Cf. A000225 (for skip 1 take 1), A182459 (for skip 2 take 1).

Extensions

More terms from Jinyuan Wang, Jul 01 2025