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

1,1

Comments

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

Links

Table of n, a(n) for n=1..38.

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(A333244(n)).

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

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

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

Example

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

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]

Prog

(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

Crossrefs

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

Sequence in context: A000565 A014930 A196988 * A061252 A096049 A166488

Adjacent sequences: A358176 A358177 A358178 * A358180 A358181 A358182

Keyword

nonn

Author

Michael P. May, Nov 11 2022

Status

approved