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A365573
Number of primes between prime(n) and prime(n)+log(prime(n)), exclusive.
1
0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 2, 2, 1, 0, 0, 1, 0, 1
OFFSET
1,88
COMMENTS
Inspired by A354841.
FORMULA
Conjecture: Limit_{N->oo} (Ratio_{n=1..N} a(n)=0) = 1/e (A068985).
PROG
(PARI) a(n) = primepi(prime(n)+log(prime(n))) - primepi(prime(n))
CROSSREFS
KEYWORD
nonn
AUTHOR
Alain Rocchelli, Sep 09 2023
STATUS
approved