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%I #16 Oct 08 2022 00:02:03
%S 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,
%T 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,
%U 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
%N Start with a(0)=1, then k-th run is 1,2,3,..., a(0) + a(1) + a(2) + ... + a(k-1).
%F 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).
%e 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), ...
%Y Cf. A006893.
%K nonn
%O 0,4
%A _Benoit Cloitre_, Jul 29 2003
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