

A079851


a(1) = 1, a(2) = 2 and a(n) is the smallest number such that all a(i)*a(j) are different.


5



1, 2, 3, 5, 7, 8, 11, 13, 17, 18, 19, 23, 29, 31, 37, 41, 43, 47, 50, 53, 59, 60, 61, 67, 71, 73, 79, 81, 83, 89, 97, 98, 101, 103, 105, 107, 109, 113, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 242
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Taking a(n) as the smallest number such that a(i)+a(j) are all different gives the Fibonacci sequence (A000045) from third term onwards.
Contains all primes. Differs from A066724 in that the latter forbids only the products of distinct terms.  Ivan Neretin, Mar 02 2016


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..1000


EXAMPLE

After 5, 7 is the next member and not 6 as 6*1 = 2*3.


MAPLE

A[1]:= 1:
F:= {1}:
for n from 2 to 100 do
for k from A[n1]+1 do
Fk:= {k^2, seq(A[i]*k, i=1..n1)};
if Fk intersect F = {} then
A[n]:= k;
F:= F union Fk;
break
fi
od
od:
seq(A[i], i=1..100); # Robert Israel, Mar 02 2016


MATHEMATICA

nmax = 100; a[1] = 1; F = {1};
For[n = 2, n <= nmax, n++,
For[k = a[n1]+1, True, k++, Fk = Join[{k^2}, Table[a[i]*k, {i, 1, n1}]] // Union; If[Fk ~Intersection~ F == {}, a[n] = k; F = F ~Union~ Fk; Break[]
]]];
Array[a, nmax] (* JeanFrançois Alcover, Mar 26 2019, after Robert Israel *)


CROSSREFS

Cf. A000045, A079850, A079852, compare to A066724.
Sequence in context: A319239 A026410 A066720 * A060634 A279457 A171561
Adjacent sequences: A079848 A079849 A079850 * A079852 A079853 A079854


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Feb 19 2003


EXTENSIONS

Corrected and extended by Ray Chandler, Feb 12 2007
Corrected by Ivan Neretin, Mar 02 2016


STATUS

approved



