A358179 Prime numbers with prime indices in A333244.

31, 709, 1787, 8527, 19577, 27457, 42043, 52711, 72727, 96797, 112129, 137077, 167449, 173867, 239489, 250751, 285191, 352007, 401519, 443419, 464939, 490643, 527623, 683873, 718807, 755387, 839483, 864013, 985151, 1021271, 1080923, 1128889, 1159901, 1278779, 1323503, 1342907, 1656649, 1693031

Offset: 1

Author

Michael P. May, Nov 11 2022

Keywords

• nonn

Comments

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

Examples

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

Links

• Michael P. May, Properties of Higher-Order Prime Number Sequences, Missouri J. Math. Sci. (2020) Vol. 32, No. 2, 158-170; and arXiv version, arXiv:2108.04662 [math.NT], 2021.

Crossrefs

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

Programs

Mathematica

b[n_] := b[n] = If[PrimeQ[n], 1+b[PrimePi[n]], 0];
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];
Array[a, 50]

PARI

b(n)={my(k=0); while(isprime(n), k++; n=primepi(n)); k};
apply(x->prime(prime(prime(prime(x)))), select(n->b(n)%2, [1..500])) \\ Michel Marcus, Nov 18 2022

Formula

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

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

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

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