A333243 Prime numbers with prime indices in A262275.

5, 31, 59, 179, 331, 431, 599, 709, 919, 1153, 1297, 1523, 1787, 1847, 2381, 2477, 2749, 3259, 3637, 3943, 4091, 4273, 4549, 5623, 5869, 6113, 6661, 6823, 7607, 7841, 8221, 8527, 8719, 9461, 9739, 9859, 11743, 11953, 12097, 12301, 12547, 13469, 13709, 14177

Offset: 1

Author

Michael P. May, Mar 12 2020

Keywords

• nonn

Comments

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

Examples

			a(1) = prime(A262275(1)) = prime(3) = 5.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael P. May, On the Properties of Special Prime Number Subsequences, arXiv:1608.08082 [math.GM], 2016-2020.
• 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, A333244.

Programs

Maple

b:= proc(n) option remember;
      `if`(isprime(n), 1+b(numtheory[pi](n)), 0)
    end:
a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
        if (h-> h>1 and h::odd)(b(p)) then break fi
      od; p
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Mar 15 2020

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[#>1 && OddQ[#]&[b[p]], Break[]]]; p];
Array[a, 50] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

PARI

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

Formula

a(n) = prime(A262275(n)).