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Characteristic function of A333242: a(n) = 1 if n is a term of A333242.
2

%I #40 Jul 02 2024 14:43:53

%S 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,

%T 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,

%U 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

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

%C 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.

%H Antti Karttunen, <a href="/A373338/b373338.txt">Table of n, a(n) for n = 1..100000</a>

%H Michael P. May, <a href="https://doi.org/10.35834/2020/3202158">Properties of Higher-Order Prime Number Sequences</a>, Missouri J. Math. Sci. (2020) Vol. 32, No. 2, 158-170; and <a href="https://arxiv.org/abs/2108.04662">arXiv version</a>, arXiv:2108.04662 [math.NT], 2021.

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>

%F a(n) = A078442(n) mod 2

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

%o (PARI) A078442(n) = my(k=0); while(isprime(n), k++; n=primepi(n)); k;

%o a(n) = A078442(n) % 2; \\ _Michel Marcus_, Jun 15 2024

%Y Cf. A333242, A262275, A348677, A078442.

%K nonn

%O 1,1

%A _Michael P. May_, Jun 01 2024