A138528 - OEIS

%I #12 Jan 31 2018 04:00:57

%S 1,1,1,2,1,2,3,1,2,3,4,5,1,2,3,4,5,6,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,

%T 9,10,11,1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,5,6,7,8,9,10,11,12,13,14,

%U 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,2,3,4,5,6,7,8,9,10,11,12,13,14

%N a(1) = 1. The n-th run (after the initial 1) of A138529(n) terms is (1,2,3,...,A138529(n)), where A138529(n) = Sum_{k=1..n} a(k).

%H Ivan Neretin, <a href="/A138528/b138528.txt">Table of n, a(n) for n = 1..10000</a>

%e Runs (after the initial 1) each placed in parentheses:

%e (Notice that n-th run in parentheses contains exactly (Sum_{k=1..n} a(k)) terms.)

%e 1, (1), (1, 2), (1, 2, 3), (1, 2, 3, 4, 5), (1, 2, 3, 4, 5, 6), (1, 2, 3, 4, 5, 6, 7, 8), (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11), (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12), (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14), (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17), ...

%t Nest[Flatten@Join[{1}, Range[Accumulate@#]] &, {1}, 4] (* _Ivan Neretin_, Jan 30 2018 *)

%Y Cf. A138529.

%K easy,nonn

%O 1,4

%A _Leroy Quet_, Mar 23 2008