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.

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

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 20 2004

Keywords

• easy
• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A099507 for positions of occurrences of integers in this sequence.

Cf. A125717.

Programs

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

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