A348677 -id:A348677 - cp's OEIS frontend

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

Michael P. May, Jun 01 2024

nonn

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.

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

Cf. A333242, A262275, A348677, A078442.

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

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

a(n) = A078442(n) mod 2

A358274 a(n) is the prime before A262275(n).

Original entry on oeis.org

2, 7, 13, 37, 61, 79, 107, 113, 151, 181, 199, 239, 271, 281, 349, 359, 397, 457, 503, 541, 557, 577, 613, 733, 769, 787, 857, 863, 953, 983, 1021, 1061, 1069, 1163, 1193, 1213, 1399, 1429, 1439, 1459, 1493, 1583, 1619, 1667, 1721, 1733, 1811, 1907, 2017, 2053

Offset: 1

Michael P. May, Nov 11 2022

nonn

The sum of the individual gaps formed by the subtraction of the next lower prime number from each prime in A262275 approximates the prime counting function at very large n.

			a(3) = A262275(3) - A348677(3) = 17 - 4 = 13.

Michael P. May, "Relationship Between the Prime Counting Function and a Unique Prime Number Sequence", accepted for publication in the March 2023 edition of the Missouri Journal of Mathematical Sciences.

Cf. A151799, A262275, A348677.

b(n) = {my(k=0); while(isprime(n), k++; n=primepi(n)); k};
apply(x->precprime(x-1), apply(prime, select(n->b(n)%2, [1..500]))) \\ Michel Marcus, Nov 18 2022

a(n) = A262275(n) - A348677(n).

a(n) = A151799(A262275(n)).

cp's OEIS Frontend

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

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