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A094339 Beginning with 2, least number not occurring earlier that divides the sum of all previous terms.

%I A094339 #15 Apr 14 2015 07:54:14
%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,
%T A094339 265,159,318,212,14,107,321,214,428,642,535,35,21,181,11,33,22,23,59,
%U A094339 70,28,151,29,19,233,466,2563,699,932,40,26,38,31,61,39,49,98,42,56,50,197,17
%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_, 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."
%H A094339 Ivan Neretin, <a href="/A094339/b094339.txt">Table of n, a(n) for n = 1..10000</a>
%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_, Apr 30 2007
%t A094339 a={2}; Do[AppendTo[a,Min[Select[Divisors[Plus@@a],!MemberQ[a,#]&]]], {t,2,70}]; a (* _Ivan Neretin_, Apr 13 2015 *)
%o A094339 (PARI) v=[2];n=1;while(#v<100,if(!vecsearch(vecsort(v,,8),n)&&!(vecsum(v)%n),v=concat(v,n);n=0);n++);v \\ _Derek Orr_, Apr 13 2015
%Y A094339 Cf. A094340, A094341.
%K A094339 nonn
%O A094339 1,1
%A A094339 _Amarnath Murthy_, May 17 2004
%E A094339 Corrected and extended by _R. J. Mathar_, Apr 30 2007