A086742 Start with a(0)=1, then k-th run is 1,2,3,..., a(0) + a(1) + a(2) + ... + a(k-1).

1, 1, 1, 2, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47

Offset: 0

Author

Benoit Cloitre, Jul 29 2003

Keywords

• nonn

Examples

			The first 3 runs are (1), (1), (1, 2) and a(0) + a(1) + a(2) + a(3) = 1+1+1+2 = 5, so the 4th run is 1, 2, 3, 4, 5 and the sequence continues: (1), (1), (1, 2), (1, 2, 3, 4, 5), ...
		

Crossrefs

Cf. A006893.

Formula

a(0) + a(1) + a(2) + ... + a(r(k)) = A006893(k) where r(k) denotes the index of the end of the k-th run. I.e., the first 4 runs are (1), (1), (1, 2), (1, 2, 3, 4, 5), so the 4th run ends with 5=a(8), so r(4)=8 and a(0) + a(1) + a(2) + ... + a(r(4)) = 1+1+1+2+1+2+3+4+5 = 20 which is A006893(4).