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A333243 Prime numbers with prime indices in A262275.

%I A333243 #33 Nov 18 2022 09:23:39
%S A333243 5,31,59,179,331,431,599,709,919,1153,1297,1523,1787,1847,2381,2477,
%T A333243 2749,3259,3637,3943,4091,4273,4549,5623,5869,6113,6661,6823,7607,
%U A333243 7841,8221,8527,8719,9461,9739,9859,11743,11953,12097,12301,12547,13469,13709,14177
%N A333243 Prime numbers with prime indices in A262275.
%C A333243 This sequence can also be generated by the N-sieve.
%H A333243 Michael De Vlieger, <a href="/A333243/b333243.txt">Table of n, a(n) for n = 1..10000</a>
%H A333243 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 A333243 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 A333243 a(n) = prime(A262275(n)).
%e A333243 a(1) = prime(A262275(1)) = prime(3) = 5.
%p A333243 b:= proc(n) option remember;
%p A333243       `if`(isprime(n), 1+b(numtheory[pi](n)), 0)
%p A333243     end:
%p A333243 a:= proc(n) option remember; local p;
%p A333243       p:= `if`(n=1, 1, a(n-1));
%p A333243       do p:= nextprime(p);
%p A333243         if (h-> h>1 and h::odd)(b(p)) then break fi
%p A333243       od; p
%p A333243     end:
%p A333243 seq(a(n), n=1..50);  # _Alois P. Heinz_, Mar 15 2020
%t A333243 b[n_] := b[n] = If[PrimeQ[n], 1+b[PrimePi[n]], 0];
%t A333243 a[n_] := a[n] = Module[{p}, p = If[n==1, 1, a[n-1]]; While[True, p = NextPrime[p]; If[#>1 && OddQ[#]&[b[p]], Break[]]]; p];
%t A333243 Array[a, 50] (* _Jean-François Alcover_, Nov 16 2020, after _Alois P. Heinz_ *)
%o A333243 (PARI) b(n)={my(k=0); while(isprime(n), k++; n=primepi(n)); k};
%o A333243 apply(x->prime(prime(x)), select(n->b(n)%2, [1..500])) \\ _Michel Marcus_, Nov 18 2022
%Y A333243 Cf. A078442, A262275, A333242, A333244.
%K A333243 nonn
%O A333243 1,1
%A A333243 _Michael P. May_, Mar 12 2020