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
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
Programs
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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