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

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

Author

Michael P. May, Nov 11 2022

Keywords

• nonn

Comments

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.

Examples

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

References

• 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.

Crossrefs

Cf. A151799, A262275, A348677.

Programs

PARI

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

Formula

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

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