A381901 Partition the natural numbers by letting a(1)=1 (denoting the set {1}) and for n>1 define a(n) to be the least integer such that the product of the set of integers {a(n-1)+1,...,a(n)} is an integer multiple of the previous partition's product.

1, 2, 4, 8, 14, 26, 46, 86, 166, 326, 634, 1262, 2518, 5006, 10006, 19946, 39874, 79738, 159398, 318778, 637502, 1274998, 2549978, 5099902, 10199786, 20399534, 40799062, 81598082, 163196134, 326392258, 652784498, 1305568942, 2611137838, 5222275634, 10444551254

Offset: 1

Author

Andy Niedermaier, Mar 09 2025

Keywords

• nonn

Examples

			The first few corresponding partitions are {1}, {2}, {3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12, 13, 14}.
		

Crossrefs

Cf. A006992, A090905.

Appears to agree with A113117 starting at the 5th term and with A113118 starting at the 6th term.

Formula

a(n) = A090905(n+1) - 1.

a(n) = 2 * A006992(n-1) for n>=5.