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%I #50 Sep 28 2019 14:34:39
%S 2,4,5,8,10,13,16,17,20,23,25,26,31,32,34,37,40,43,46,47,50,52,61,62,
%T 64,65,67,68,73,74,79,80,85,86,89,92,94,100,103,104,107,109,113,115,
%U 122,124,125,128,130,134,136,137,146,148,149,151,155,158,160,163
%N Lexicographically earliest infinite sequence of numbers m > 1 with the property that none of the prime indices of m are in the sequence.
%C A self-describing sequence.
%C The prime indices of m are the numbers k such that prime(k) divides m.
%C 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
%H Robert Israel, <a href="/A304360/b304360.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%p A:= NULL:
%p P:= {}:
%p for n from 2 to 1000 do
%p pn:= numtheory:-factorset(n);
%p if pn intersect P = {} then
%p A:= A, n;
%p P:= P union {ithprime(n)};
%p fi
%p od:
%p A; # _Robert Israel_, Aug 26 2018
%t gaQ[n_]:=Or[n==0,And@@Cases[FactorInteger[n],{p_,k_}:>!gaQ[PrimePi[p]]]];
%t Select[Range[100],gaQ]
%Y Cf. A000002, A001462, A079000, A079254, A214577, A276625, A277098, A280996, A303431.
%Y For first differences see A317963, for primes see A317964.
%K nonn
%O 1,1
%A _Gus Wiseman_, Aug 16 2018
%E Added "infinite" to definition. - _N. J. A. Sloane_, Sep 28 2019
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