A333244 Prime numbers with prime indices in A333243.

11, 127, 277, 1063, 2221, 3001, 4397, 5381, 7193, 9319, 10631, 12763, 15299, 15823, 21179, 22093, 24859, 30133, 33967, 37217, 38833, 40819, 43651, 55351, 57943, 60647, 66851, 68639, 77431, 80071, 84347, 87803, 90023, 98519, 101701, 103069, 125113, 127643

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(A333243(n)).

Example

a(1) = prime(A333243(1)) = prime(5) = 11.

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>2 and h::even)(b(p)) then break fi
      od; p
    end:
seq(a(n), n=1..42);  # 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[#>2 && EvenQ[#]&[b[p]], Break[]]]; p];
Array[a, 42] (* 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(prime(x))), select(n->b(n)%2, [1..500])) \\ Michel Marcus, Nov 18 2022

Crossrefs

Cf. A078442, A262275, A333242, A333243.

Sequence in context: A156970 A174270 A335954 * A141987 A048394 A088628

Adjacent sequences: A333241 A333242 A333243 * A333245 A333246 A333247

Keyword

nonn

Author

Michael P. May, Mar 12 2020

Status

approved