%I #7 Apr 30 2014 01:30:10
%S 1,2,3,5,7,12,14,23,25,38,40,57,59,80,82,107,109,138,140,173,175,212,
%T 214,255,257,302,304,353,355,408,410,467,469,530,532,597,599,668,670,
%U 743,745,822,824,905,907,992,994,1083,1085,1178,1180,1277,1279,1380
%N a(n) = smallest m such that A100035(m) = n.
%C Smallest positions of occurrences of the natural numbers as subsequence in A100035;
%C A100035(a(n)) = n and A100035(m) <> n for m < a(n);
%C a(n) < A100037(n) < A100038(n) < A100039(n).
%F Conjecture: a(n) = partial sums of sequence [1,1,1,2,2,5,2,9,2,13,2,17,2,21,2,25,2,29,2,33,...2,n/2-7,2,...]. In other words, a(n) consists of the numbers 1,2,3 and the sequences A096376 and A096376+2 interspersed. - _Ralf Stephan_, May 15 2007
%e First terms (10=A,11=B,12=C) of A100035(a(n)):
%e 123.4.5....6.7........8.9............A.B................C.
%e 1231435425165764736271879869584938291A9BA8B7A6B5A4B3A2B1CBD;
%e a(1) = A084849(1) = 1, A100035(1) = 1;
%e a(2) = A014107(1) = 2, A100035(2) = 2;
%e a(3) = A033537(1) = 3, A100035(3) = 3;
%e a(4) = A100040(1) = 5, A100035(5) = 4;
%e a(5) = A100041(1) = 7, A100035(7) = 5.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Oct 31 2004