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A333244 Prime numbers with prime indices in A333243.

%I A333244 #30 Nov 18 2022 09:23:35
%S A333244 11,127,277,1063,2221,3001,4397,5381,7193,9319,10631,12763,15299,
%T A333244 15823,21179,22093,24859,30133,33967,37217,38833,40819,43651,55351,
%U A333244 57943,60647,66851,68639,77431,80071,84347,87803,90023,98519,101701,103069,125113,127643
%N A333244 Prime numbers with prime indices in A333243.
%C A333244 This sequence can also be generated by the N-sieve.
%H A333244 Michael De Vlieger, <a href="/A333244/b333244.txt">Table of n, a(n) for n = 1..10000</a>
%H A333244 Michael P. May, <a href="https://arxiv.org/abs/1608.08082">On the Properties of Special Prime Number Subsequences</a>, arXiv:1608.08082 [math.GM], 2016-2020.
%H A333244 Michael P. May, <a href="https://doi.org/10.35834/2020/3202158">Properties of Higher-Order Prime Number Sequences</a>, Missouri J. Math. Sci. (2020) Vol. 32, No. 2, 158-170; and <a href="https://arxiv.org/abs/2108.04662">arXiv version</a>, arXiv:2108.04662 [math.NT], 2021.
%F A333244 a(n) = prime(A333243(n)).
%e A333244 a(1) = prime(A333243(1)) = prime(5) = 11.
%p A333244 b:= proc(n) option remember;
%p A333244       `if`(isprime(n), 1+b(numtheory[pi](n)), 0)
%p A333244     end:
%p A333244 a:= proc(n) option remember; local p;
%p A333244       p:= `if`(n=1, 1, a(n-1));
%p A333244       do p:= nextprime(p);
%p A333244         if (h-> h>2 and h::even)(b(p)) then break fi
%p A333244       od; p
%p A333244     end:
%p A333244 seq(a(n), n=1..42);  # _Alois P. Heinz_, Mar 15 2020
%t A333244 b[n_] := b[n] = If[PrimeQ[n], 1+b[PrimePi[n]], 0];
%t A333244 a[n_] := a[n] = Module[{p}, p = If[n==1, 1, a[n-1]]; While[True, p = NextPrime[p]; If[#>2 && EvenQ[#]&[b[p]], Break[]]]; p];
%t A333244 Array[a, 42] (* _Jean-François Alcover_, Nov 16 2020, after _Alois P. Heinz_ *)
%o A333244 (PARI) b(n)={my(k=0); while(isprime(n), k++; n=primepi(n)); k};
%o A333244 apply(x->prime(prime(prime(x))), select(n->b(n)%2, [1..500])) \\ _Michel Marcus_, Nov 18 2022
%Y A333244 Cf. A078442, A262275, A333242, A333243.
%K A333244 nonn
%O A333244 1,1
%A A333244 _Michael P. May_, Mar 12 2020