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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[n-1]+1 do

    Fk:= {k^2, seq(A[i]*k, i=1..n-1)};

    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[n-1]+1, True, k++, Fk = Join[{k^2}, Table[a[i]*k, {i, 1, n-1}]] // Union; If[Fk ~Intersection~ F == {}, a[n] = k; F = F ~Union~ Fk; Break[]

]]];

Array[a, nmax] (* Jean-Fran├žois 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

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Last modified April 23 03:26 EDT 2019. Contains 322380 sequences. (Running on oeis4.)