A339959 Number of times the n-th prime (=A000040(n)) occurs in A033932.

0, 0, 1, 2, 2, 0, 1, 1, 2, 2, 3, 2, 1, 2, 1, 3, 1, 2, 3, 3, 1, 1, 2, 1, 5, 2, 1, 4, 1, 3, 4, 6, 1, 2, 3, 0, 1, 0, 1, 0, 0, 3, 2, 1, 1, 1, 0, 3, 4, 5, 1, 5, 5, 0, 3, 0, 0, 8, 1, 0, 5, 2, 3, 2, 1, 4, 5, 1, 1, 1, 2, 1, 2, 0, 2, 2, 3, 4, 3, 2, 0, 6, 1, 1, 4, 4

Offset

1,4

Comments

Each term in A033932 is either 1 or a prime number. Moreover, it is known that each prime occurs only a finite number of times in A033932.

By excluding the terms that equal one from A033932, we observe the smallest value of A033933(n)/log(n!) in the range n = 2..4000 to be ~0.1399. From this it is believed that the primes less than 0.9*log(4001!)*0.1399 (~ 3676) will not occur anymore in the sequence A033932 for n > 4000; the applied factor 0.9 is a safety factor to be more or less sure that the prime numbers up to about 3676 will no longer occur in A033932 for n > 4000.

Links

A.H.M. Smeets, Table of n, a(n) for n = 1..512

A.H.M. Smeets, Sum_{k = 1..n} a(k) versus A000040(n)

Formula

It seems that Sum_{k = 1..n} a(k) ~ 0.7*A000040(n)/log(log(A000040(n))).

Example

The prime number 11 occurs 2 times in A033932, and A000040(5) = 11, so a(5) = 2.

Crossrefs

Cf. A000040, A033932, A033933.

Sequence in context: A113414 A286653 A283308 * A255636 A292085 A262163

Adjacent sequences: A339956 A339957 A339958 * A339960 A339961 A339962

Keyword

nonn

Author

A.H.M. Smeets, Dec 25 2020

Status

approved