%I A094339
%S A094339 2,1,3,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53,106,265,
%T A094339 159,318,212,14,107,321,214,428,642,535,35,21,181,11,33,22,23,59,70,28,
%U A094339 151,29,19,233,466,2563,699,932,40,26,38,31,61,39,49,98,42,56,50,197,17
%N A094339 Beginning with 2, least number not occurring earlier that divides the 
               sum of all previous terms.
%C A094339 Conjecture: this is a rearrangement of natural numbers.
%C A094339 Comments from Zak Seidov (zakseidov(AT)yahoo.com), Feb 19 2005:
%C A094339 "Changing the seed produces different sequences, some of which merge 
               into each other:
%C A094339 s2=2,1,3,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53
%C A094339 s3=3,1,2,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53
%C A094339 s4=4,1,5,2,3,15,6,9,45,10,20,8,16,12,13,169,26,7,53,106,265,159,18
%C A094339 s5=5,1,2,4,3,15,6,9,45,10,20,8,16,12,13,169,26,7,53,106,265,159,18
%C A094339 s6=6,1,7,2,4,5,25,10,3,9,8,16,12,18,14,20,32,24,27,81,36,15,75,30,40
%C A094339 s7=7,1,2,5,3,6,4,14,21,9,8,10,15,35,20,16,11,17,12,18,13,19,38,76,95
%C A094339 s8=8,1,3,2,7,21,6,4,13,5,10,16,12,9,39,26,14,28,32,64,20,17,51,24,18
%C A094339 s9=9,1,2,3,5,4,6,10,8,12,15,25,20,24,16,32,48,30,18,36,27,13,7,53,106
%C A094339 s10=10,1,11,2,3,9,4,5,15,6,22,8,12,18,7,19,38,95,57,114,24,16,31,17,32
%C A094339 s11=11,1,2,7,3,4,14,6,8,28,12,16,56,21,9,18,24,5,35,10,29,319,22,15,25,
               20,30
%C A094339 In every case one may ask if the result is a rearrangement of the natural 
               numbers."
%e A094339 The sum of first 7 terms is 36, hence a(8) = 9 is the least divisor of 
               36 not occurring earlier.
%p A094339 A094339 := proc(nmax) local a,n,sprev,i; a := [2] ; while nops(a) < nmax 
               do sprev := add(i,i=a) ; n := 1 ; while sprev mod n <> 0 or n in 
               a do n := n+1 ; od ; a := [op(a),n] ; od ; RETURN(a) ; end: A094339(100) 
               ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 30 2007
%Y A094339 Cf. A094340, A094341.
%Y A094339 Sequence in context: A125205 A125206 A133904 this_sequence A120576 A063707 
               A118287
%Y A094339 Adjacent sequences: A094336 A094337 A094338 this_sequence A094340 A094341 
               A094342
%K A094339 nonn
%O A094339 1,1
%A A094339 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 17 2004
%E A094339 Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Apr 30 2007