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

1,1

Comments

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

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.

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A078442, A262275, A333242, A333244.

Sequence in context: A147033 A125743 A332788 * A078686 A031908 A139862

Adjacent sequences: A333240 A333241 A333242 * A333244 A333245 A333246

Keyword

nonn

Author

Michael P. May, Mar 12 2020

Status

approved