A358179 - OEIS

%I #34 Nov 22 2022 11:56:21

%S 31,709,1787,8527,19577,27457,42043,52711,72727,96797,112129,137077,

%T 167449,173867,239489,250751,285191,352007,401519,443419,464939,

%U 490643,527623,683873,718807,755387,839483,864013,985151,1021271,1080923,1128889,1159901,1278779,1323503,1342907,1656649,1693031

%N Prime numbers with prime indices in A333244.

%C This sequence can also be generated by the N-sieve.

%H 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 a(n) = prime(A333244(n)).

%F a(n) = A049090(A333242(n)).

%F a(n) = A038580(A262275(n)).

%F a(n) = A006450(A333243(n)).

%e a(1) = prime(A333244(1)) = prime(11) = 31.

%t b[n_] := b[n] = If[PrimeQ[n], 1+b[PrimePi[n]], 0];

%t a[n_] := a[n] = Module[{p}, p = If[n==1, 1, a[n-1]]; While[True, p = NextPrime[p]; If[#>3 && OddQ[#]&[b[p]], Break[]]]; p];

%t Array[a, 50]

%o (PARI) b(n)={my(k=0); while(isprime(n), k++; n=primepi(n)); k};

%o apply(x->prime(prime(prime(prime(x)))), select(n->b(n)%2, [1..500])) \\ _Michel Marcus_, Nov 18 2022

%Y Cf. A078442, A262275, A333242, A333243, A333244.

%K nonn

%O 1,1

%A _Michael P. May_, Nov 11 2022