OFFSET
1,1
COMMENTS
A self-describing sequence.
The prime indices of m are the numbers k such that prime(k) divides m.
The sequence is monotonically increasing, since once a number is rejected it stays rejected. Sequence is closed under multiplication for a similar reason. - N. J. A. Sloane, Aug 26 2018
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
After the initial term 2, the next term cannot be 3 because 3 has prime index 2, and 2 is already in the sequence. The next term could be 10, which has prime indices 1 and 3, but 4 (with prime index 1) is smaller. So a(2) = 4.
MAPLE
A:= NULL:
P:= {}:
for n from 2 to 1000 do
pn:= numtheory:-factorset(n);
if pn intersect P = {} then
A:= A, n;
P:= P union {ithprime(n)};
fi
od:
A; # Robert Israel, Aug 26 2018
MATHEMATICA
gaQ[n_]:=Or[n==0, And@@Cases[FactorInteger[n], {p_, k_}:>!gaQ[PrimePi[p]]]];
Select[Range[100], gaQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 16 2018
EXTENSIONS
Added "infinite" to definition. - N. J. A. Sloane, Sep 28 2019
STATUS
approved