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 A099506 a(1)=1; for n > 1, a(n)=smallest m>0 that has not appeared so far in the sequence such that m+a(n-1) is a multiple of n. 7
 1, 3, 6, 2, 8, 4, 10, 14, 13, 7, 15, 9, 17, 11, 19, 29, 5, 31, 26, 34, 50, 16, 30, 18, 32, 20, 61, 23, 35, 25, 37, 27, 39, 63, 42, 66, 45, 69, 48, 72, 51, 33, 53, 79, 56, 36, 58, 38, 60, 40, 62, 94, 12, 96, 124, 44, 70, 46, 131, 49, 73, 113, 76, 52, 78, 54, 80, 192, 84, 126, 87 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(1)=1 by definition. a(2)=3 because then a(2)+a(1)=3+1=4 which is a multiple of 2. a(2) cannot be 1 (which would lead to a sum of 2) because this has already appeared. Likewise, a(3)=6 so that a(3)+a(2)=6+3=9 which is a multiple of 3. a(4)=2 so that a(4)+a(3)=2+6=8 and so on. PROG (PARI) v=[1]; n=1; while(n<100, s=n+v[#v]; if(!(s%(#v+1)||vecsearch(vecsort(v), n)), v=concat(v, n); n=0); n++); v \\ Derek Orr, Jun 16 2015 (MATLAB) N = 100; M = 10*N;  % find a(1) to a(N) or until a(n) > M B = zeros(1, M); A = zeros(1, N); mmin = 2; A(1) = 1; B(1) = 1; for n = 2:N   for m = mmin:M     if mmin == m && B(m) == 1        mmin = mmin+1;     elseif B(m) == 0 && rem(m + A(n-1), n) == 0       A(n) = m;       B(m) = 1;       if m == mmin          mmin = mmin + 1;       end;       break     end;   end;   if A(n) == 0      break   end end; if A(n) == 0   A(1:n-1) else   A end; % Robert Israel, Jun 17 2015 CROSSREFS Cf. A099507 for positions of occurrences of integers in this sequence. Sequence in context: A175458 A135598 A244619 * A205001 A154204 A266971 Adjacent sequences:  A099503 A099504 A099505 * A099507 A099508 A099509 KEYWORD easy,nonn AUTHOR Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 20 2004 STATUS approved

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