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Lexicographically earliest infinite sequence of numbers m > 1 with the property that none of the prime indices of m are in the sequence.
64

%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