A076105 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 a multiple of the sum of the previous row.

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, 47, 26, 27, 28, 29, 30, 31, 32, 157, 33, 34, 35, 36, 37, 38, 39, 40, 68, 41, 42, 43, 45, 46, 48, 49, 50, 51, 305, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 155, 62, 63, 64, 65, 66, 67

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 A094280 is defined similarly, but the sum of the next row must be greater than that of the current row.

Links

Table of n, a(n) for n=1..72.

Index entries for sequences that are permutations of the natural numbers

Example

1;
2,  3;
4,  5,  6;
7,  8,  9,  21;
10, 11, 12, 13, 44;
14, 15, 16, 17, 18, 100;

Crossrefs

Inverse: A122154. Cf. A076101, A076102, A076103, A076104.

Sequence in context: A079170 A330927 A319387 * A094280 A082323 A069571

Adjacent sequences: A076102 A076103 A076104 * A076106 A076107 A076108

Keyword

nonn,tabl

Author

Amarnath Murthy, Oct 08 2002

Extensions

More terms from David Wasserman, Apr 02 2005

Description edited by Antti Karttunen, Aug 25 2006

Status

approved