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
KEYWORD
nonn
AUTHOR
Michael P. May, Mar 12 2020
STATUS
approved