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

1,2

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.

Cf. A125717.

Sequence in context: A135598 A244619 A330576 * A205001 A154204 A309609

Adjacent sequences: A099503 A099504 A099505 * A099507 A099508 A099509

Keyword

easy,nonn

Author

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

Status

approved