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A340007
Number of times the n-th prime (=A000040(n)) occurs in A038711.
3
0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 3, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 4, 0, 0, 0, 1, 0, 0, 1, 1, 2, 0, 1, 1, 0, 1, 2, 0, 0, 2, 1
OFFSET
1,18
COMMENTS
Each term in A038711 is either 1 or a prime number. Moreover it is known that each prime occurs only a finite number of times in A038711.
By excluding the terms that equal one from A038711, we observe the smallest value of A038711(n)/log(A002110(n)) in the range n = 2..1000 to be ~1.017. From this it is believed that the primes less than 0.9*log(A002110(1001))*1.017 (~ 7157) will not occur anymore in the sequence A038711 for n > 1000; the applied factor 0.9 is a safety factor to be more or less sure that the prime numbers up to about 7157 will no longer occur in A038711.
FORMULA
It seems that Sum_{k = 1..n} a(k) ~ 0.7*A000040(n)/log(log(A000040(n))).
EXAMPLE
The prime number 17 occurs 1 time in A038711, and A000040(7) = 17, so a(7) = 1.
The prime number 5 does not occur in A038711, and A000040(3) = 5, so a(3) = 0.
CROSSREFS
See also A339274, A339959 (n!).
Sequence in context: A374213 A140807 A232629 * A091959 A318659 A318513
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Dec 26 2020
STATUS
approved