A107609 -id:A107609 - cp's OEIS frontend

A079416 a(n) = round(prime(n)/n).

2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Reinhard Zumkeller, Jan 07 2003

nonn

The sequence is not monotone, see example and A079417.

			a(20) = round(prime(20)/20) = round(71/20) = round(3.55) = 4;
a(21) = round(prime(21)/21) = round(73/21) = round(3.476190...) = 3;
a(22) = round(prime(22)/22) = round(79/22) = round(3.590909...) = 4.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A079418, A000040, A038605, A107609, A263076.

[Round(NthPrime(n)/n): n in [1..100]]; // G. C. Greubel, Jan 18 2019

f[n_] := Round[ Prime[n]/n]; Array[f, 105] (* Robert G. Wilson v, Oct 23 2015 *)

vector(100, n, round(prime(n)/n)) \\ G. C. Greubel, Jan 18 2019

[round(nth_prime(n)/n) for n in (1..100)] # G. C. Greubel, Jan 18 2019

A107610 Least number k such that round(k/pi(k)) = n.

Original entry on oeis.org

2, 16, 56, 190, 556, 1821, 4928, 14136, 39017, 107405, 291330, 791513, 2148323, 5797898, 15726486, 42605113, 115371428, 312629484, 847000031, 2295700537, 6223257066, 16874397811, 45764114391, 124142354193, 336811260666

Offset: 2

Jonathan Vos Post and Robert G. Wilson v, May 17 2005

nonn

a(n) is the index of the first occurrence of n in A107609.

Lim_{n->infinity} a(n+1)/a(n) ~ e.

			a(2) = 16 because round(16/pi(16)) = round(16/6) = 3 and for no number less than 16 does the quotient equal 3.

Cf. A000720, A107609, A107614, A272231.

f[n_] := Round[ n / PrimePi[ n]]; g[2] = 2; g[n_] := g[n] = Block[{k = PrimePi[E g[n - 1]]}, While[ f[k] < n, k++ ]; k]; Do[ Print[ g[ n]], {n, 2, 26}]

a(n) = min { k >= 2 : round(k/pi(k)) = n }.

A107614 Consider the least number n such that n divided by pi(n) rounded is greater than any previous n; a(n) is the denominator of n/pi(n).

Original entry on oeis.org

1, 6, 16, 42, 101, 280, 657, 1663, 4107, 10229, 25333, 63321, 159135, 399855, 1014612, 2582128, 6592653, 16898891, 43435899, 111985392, 289453817, 749973236, 1947409123, 5067034865, 13208284732, 34487824962, 90192879037

Offset: 2

Jonathan Vos Post and Robert G. Wilson v, May 17 2005

nonn

Lim_{n->infinity} a(n+1)/a(n) ~ e.

Cf. A000720, A107609, A107610.

f[n_] := Round[ n / PrimePi[ n]]; g[2] = 2; g[n_] := g[n] = Block[{k = PrimePi[E g[n - 1]]}, While[ f[k] < n, k++ ]; k]; Do[ Print[ g[ n]], {n, 2, 26}]; PrimePi[ g[ # ]] & /@ Range[2, 28]

a(n) = A000720(A107610(n)).

A272231 a(n) = round(n / pi(n)), where pi(n) is the prime-counting function.

Original entry on oeis.org

2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 2

Benjamin Przybocki, Apr 22 2016

nonn

This sequence grows slowly; a(n) reaches 10 at n = 39017.

Cf. A000720, A064658, A107609.

Table[Round[n/PrimePi@ n], {n, 2, 120}] (* Michael De Vlieger, May 20 2016 *)

n \/ primepi(n) \\ Charles R Greathouse IV, Apr 30 2016

a(n) = round(n / pi(n)).

a(n) ~ log(n). - Charles R Greathouse IV, Apr 30 2016

cp's OEIS Frontend

A079416 a(n) = round(prime(n)/n).

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A107610 Least number k such that round(k/pi(k)) = n.

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A107614 Consider the least number n such that n divided by pi(n) rounded is greater than any previous n; a(n) is the denominator of n/pi(n).

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A272231 a(n) = round(n / pi(n)), where pi(n) is the prime-counting function.

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