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A358274
a(n) is the prime before A262275(n).
0
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
1,1
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.
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.
FORMULA
a(n) = A262275(n) - A348677(n).
a(n) = A151799(A262275(n)).
EXAMPLE
a(3) = A262275(3) - A348677(3) = 17 - 4 = 13.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael P. May, Nov 11 2022
STATUS
approved