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A051484 a(n) is the next natural number (besides 1) which is not congruent to a(i) mod a(j) for any i < j < n.

%I A051484 #20 Oct 08 2018 05:57:00
%S A051484 0,2,3,7,13,19,25,43,61,109,139,151,181,187,229,295,337,487,505,517,
%T A051484 565,571,643,655,685,823,883,901,985,1189,1243,1279,1285,1429,1441,
%U A051484 1597,1621,1639,1699,1735,1741,1867,1915,1933,2101,2143,2155,2167,2371
%N A051484 a(n) is the next natural number (besides 1) which is not congruent to a(i) mod a(j) for any i < j < n.
%C A051484 What is the asymptotic distribution of these numbers?
%C A051484 All elements from 7 onward seem to be either 1 or 7 modulo 12. - _Walter Kehowski_, Oct 08 2005
%C A051484 The initial 3 terms force all subsequent terms to be congruent to 1 modulo 6. - _Charlie Neder_, Oct 07 2018
%H A051484 T. D. Noe, <a href="/A051484/b051484.txt">Table of n, a(n) for n = 1..1000</a>
%e A051484 5 is congruent to 2 (mod 3), so 5 cannot be in the sequence. 25 mod 2 (resp. 3, 7, 13, 19) gives 1 (resp. 1, 4, 12, 6), which is not in the sequence.
%p A051484 M:=[0,2]: for z to 1 do for n from 3 to 5000 do b:=true; for j from 1 to nops(M)-1 do for k from j+1 to nops(M) do if M[j] = n mod M[k] then b:=false; break; fi od od; if b then M:=[op(M),n] fi; od; od; M; # _Walter Kehowski_, Oct 08 2005
%t A051484 a[1] = 0; a[2] = 2; a[n_] := a[n] = Block[{k = a[n - 1] + 1, t = a[ # ] & /@ Range[n - 1]}, While[ Intersection[t, Union[ Mod[k, Rest[ t]]]] != {}, k++ ]; k]; Table[ a[n], {n, 50}] (* _Robert G. Wilson v_, Oct 19 2005 *)
%K A051484 easy,nonn,nice
%O A051484 1,2
%A A051484 H. Tracy Hall (hthall(AT)math.berkeley.edu)
%E A051484 More terms from _Walter Kehowski_, Oct 08 2005