A373338 Characteristic function of A333242: a(n) = 1 if n is a term of A333242.

0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

Offset: 1

Author

Michael P. May, Jun 01 2024

Keywords

• nonn

Comments

This sequence is the result of applying the N-sieve to generate the prime number subsequence A333242 where 1 indicates a prime number chosen to be included in sequence A333242 and 0 indicates the prime numbers and composites not in A333242.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• 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.
• Index entries for characteristic functions
• Index entries for sequences related to prime indices in the factorization of n

Crossrefs

Cf. A333242, A262275, A348677, A078442.

Programs

Mathematica

Select[Prime@ Range@ 75, EvenQ@ Length@ NestWhileList[ PrimePi, #, PrimeQ] &]

PARI

A078442(n) = my(k=0); while(isprime(n), k++; n=primepi(n)); k;
a(n) = A078442(n) % 2; \\ Michel Marcus, Jun 15 2024

Formula

a(n) = A078442(n) mod 2