A094280 a(1)=1 (first row) and then the n-th row of this triangle contains the least set of n unused natural numbers whose sum is k * the sum of the previous row, with k being an integer > 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 10, 11, 12, 13, 44, 14, 15, 16, 17, 18, 100, 19, 20, 22, 23, 24, 25, 227, 26, 27, 28, 29, 30, 31, 32, 517, 33, 34, 35, 36, 37, 38, 39, 40, 1148, 41, 42, 43, 45, 46, 47, 48, 49, 50, 2469, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 5205, 61

Offset

1,2

Comments

The first (n-1) terms of the n-th row contain n-1 smallest natural numbers which have not occurred earlier and the last term is chosen to satisfy the requirement. Permutation A076105 is defined similarly, but k is allowed to be 1.

Links

Table of n, a(n) for n=1..67.

Index entries for sequences that are permutations of the natural numbers

Example

Sixth row (14,15,16,17,18,100) has the sum 180 and by taking the next six least unused terms: (19,20,22,23,24,25), their sum is 133, for which 227 is the first unused term, so that sum 133+227 = 360 is a multiple of 180.

Crossrefs

Inverse: A122156. Permutation A076105 is defined almost similarly. Cf. A094281, A094282, A094283, A094284.

Sequence in context: A330927 A319387 A076105 * A082323 A069571 A039173

Adjacent sequences: A094277 A094278 A094279 * A094281 A094282 A094283

Keyword

nonn,tabl

Author

Amarnath Murthy, Apr 27 2004

Extensions

Edited, extended and Scheme code added by Antti Karttunen, Aug 25 2006

Status

approved