OFFSET
1,1
COMMENTS
This sequence can also be generated by the N-sieve.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
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.
Michael P. May, Approximating the Prime Counting Function via an Operation on a Unique Prime Number Subsequence, arXiv:2112.08941 [math.GM], 2021.
Michael P. May, Relationship Between the Prime-Counting Function and a Unique Prime Number Sequence, Missouri J. Math. Sci. (2023), Vol. 35, No. 1, 105-116.
Michael P. May, Application of the Inclusion-Exclusion Principle to Prime Number Subsequences, arXiv:2402.13214 [math.GM], 2024.
FORMULA
{ p in primes : A078442(p) mod 2 = 1 }.
MAPLE
b:= proc(n) option remember;
`if`(isprime(n), 1+b(numtheory[pi](n)), 0)
end:
a:= proc(n) option remember; local p; p:= a(n-1);
do p:= nextprime(p);
if b(p)::odd then break fi
od; p
end: a(1):=2:
seq(a(n), n=1..60); # Alois P. Heinz, Mar 15 2020
MATHEMATICA
Select[Prime@ Range@ 75, EvenQ@ Length@ NestWhileList[ PrimePi, #, PrimeQ] &] (* Giovanni Resta, Mar 15 2020 *)
PROG
(PARI) \\ here b(n) is A078442.
b(n)={my(k=0); while(isprime(n), k++; n=primepi(n)); k}
select(n->b(n)%2, [1..500]) \\ Andrew Howroyd, Mar 15 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael P. May, Mar 12 2020
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Mar 15 2020
STATUS
approved