A241811 a(1) = 1, a(2) = 0; for n >= 3, a(n) = least number not included earlier that divides the concatenation of all previous terms.

1, 0, 2, 3, 11, 71, 29, 9, 683, 67, 7, 743, 739, 1933, 23, 161, 21, 37, 19, 17, 119, 49, 332534262883, 13, 39, 13739483941387, 83, 111, 79853560395691, 5431567, 70610371, 69, 51, 4112497, 28384496881337963, 353, 77, 1531, 42787, 63, 27, 41, 709, 33, 81, 487, 139697

Offset: 1

Author

Paolo P. Lava, Apr 29 2014

Keywords

• nonn
• base

Examples

			a(1)=1 and a(2)=0. a(1) U a(2) = 10 and its divisors are 1, 2, 5, 10. Therefore 2 is the least number not yet present in the sequence which divides 10. Again, a(1) U a(2) U a(3) = 102 and its divisors are 1, 2, 3, 6, 17, 34, 51, 102. Therefore a(4)=3, etc.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..68

Crossrefs

Cf. A096097, A096098, A240588.

Programs

Maple

with(numtheory):
T:=proc(t) local x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a,b,c,k,n; b:=10; print(1); print(0); c:=[0,1];
for n from 1 to q do a:=sort([op(divisors(b))]); for k from 2 to nops(a) do
if not member(a[k],c) then c:=[op(c),a[k]]; b:=a[k]+b*10^T(a[k]); print(a[k]); break;
fi; od; od; end: P(30);

Extensions

a(23)-a(28) from Zak Seidov, May 08 2014

a(29)-a(47) from Giovanni Resta, Aug 15 2019