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.

0, 2, 3, 7, 13, 19, 25, 43, 61, 109, 139, 151, 181, 187, 229, 295, 337, 487, 505, 517, 565, 571, 643, 655, 685, 823, 883, 901, 985, 1189, 1243, 1279, 1285, 1429, 1441, 1597, 1621, 1639, 1699, 1735, 1741, 1867, 1915, 1933, 2101, 2143, 2155, 2167, 2371

Offset: 1

Author

H. Tracy Hall (hthall(AT)math.berkeley.edu)

Keywords

• easy
• nonn
• nice

Comments

What is the asymptotic distribution of these numbers?

All elements from 7 onward seem to be either 1 or 7 modulo 12. - Walter Kehowski, Oct 08 2005

The initial 3 terms force all subsequent terms to be congruent to 1 modulo 6. - Charlie Neder, Oct 07 2018

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Programs

Maple

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

Mathematica

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 *)

Extensions

More terms from Walter Kehowski, Oct 08 2005