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A333242 Prime numbers with an odd number of steps in their prime index chain. 5
2, 5, 7, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 331, 337, 347, 349, 359, 373 (list; graph; refs; listen; history; text; internal format)
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.

FORMULA

{ p in primes : A078442(p) mod 2 = 1 }.

a(n) = A000720(A262275(n)). - Andrew Howroyd, Mar 15 2020

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

Cf. A000040, A000720, A078442, A262275 (complement in primes), A333243, A333244.

Sequence in context: A169690 A144300 A258430 * A045353 A038985 A109652

Adjacent sequences:  A333239 A333240 A333241 * A333243 A333244 A333245

KEYWORD

nonn

AUTHOR

Michael P. May, Mar 12 2020

EXTENSIONS

Terms a(21) and beyond from Andrew Howroyd, Mar 15 2020

STATUS

approved

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Last modified May 12 05:30 EDT 2021. Contains 343812 sequences. (Running on oeis4.)