A317964 - OEIS

%I #12 Mar 19 2019 23:00:27

%S 2,5,13,17,23,31,37,43,47,61,67,73,79,89,103,107,109,113,137,149,151,

%T 163,167,179,181,193,197,223,227,233,241,251,257,263,269,271,277,281,

%U 307,317,347,349,353,359,379,383,389,397,419,421,431,433,449,457,463,467,487,499,503,509,521,523,547

%N Prime numbers in the lexicographically earliest sequence of positive integers whose prime indices are not already in the sequence (A304360).

%C Also primes whose prime index is not in A304360, or is in A324696. A prime index of n is a number m such that prime(m) divides n. - _Gus Wiseman_, Mar 19 2019

%H Robert Israel, <a href="/A317964/b317964.txt">Table of n, a(n) for n = 1..10000</a>

%p count:= 0:

%p P:= {}: A:= NULL:

%p for n from 2 while count < 100 do

%p   pn:= numtheory:-factorset(n);

%p   if pn intersect P = {} then

%p     P:= P union {ithprime(n)};

%p     if isprime(n) then A:= A, n; count:= count+1 fi;

%p   fi

%p od:

%p A; # _Robert Israel_, Aug 26 2018

%t aQ[n_]:=n==1||Or@@Cases[FactorInteger[n],{p_,_}:>!aQ[PrimePi[p]]];

%t Prime[Select[Range[100],aQ]] (* _Gus Wiseman_, Mar 19 2019 *)

%Y Cf. A000720, A001462, A007097, A060197, A079254, A112798, A276625, A277098, A290822, A304360, A306844.

%Y Cf. A324695, A324698, A324704, A324741, A324756, A324758, A324765, A324766, A324768.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Aug 26 2018