A079416 -id:A079416 - cp's OEIS frontend

A079418 Numbers k such that prime(k)/k < prime(k-1)/(k-1).

2, 6, 8, 11, 14, 18, 21, 27, 29, 32, 34, 36, 39, 42, 44, 45, 46, 49, 50, 51, 53, 58, 60, 61, 64, 65, 66, 70, 71, 76, 79, 82, 84, 86, 89, 90, 91, 94, 96, 99, 105, 110, 113, 114, 117, 118, 121, 123, 132, 135, 137, 141, 143, 144, 145, 148, 149, 150, 152, 153, 154, 156

Offset: 1

Reinhard Zumkeller, Jan 07 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Cf. A079417, A079416, A000040, A000720.

Flatten[Position[Partition[Table[Prime[n]/n,{n,200}],2,1],?(First[#] > Last[#]&),{1},Heads->False]]+1 (* _Harvey P. Dale, Sep 10 2013 *)

a(n) = A049084(A079419(n)).

a(n) = PrimePi(A079419(n)). - Amiram Eldar, Mar 25 2025

A079417 Numbers n such that round(prime(n)/n) < round(prime(n-1)/(n-1)).

Original entry on oeis.org

21, 117, 4117, 4137, 4139, 4142, 4144, 4152, 63326, 63416, 63424, 399872, 399918, 399930, 399944, 399949, 399955, 1014615, 1014635, 1014648, 2582130, 2582200, 2582205, 2582242, 2582374, 2582437, 2582460, 2582483, 2582486, 6592657

Offset: 1

Reinhard Zumkeller, Jan 07 2003

nonn

A079416(a(n)) < A079416(a(n-1)).

Hugo Pfoertner, Table of n, a(n) for n = 1..80

A subsequence of A079418.

Cf. A000040, A079416.

Reap[For[n = 2, n <= 7*10^6, n++, If[Round[Prime[n]/n] < Round[Prime[n-1]/(n-1)], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jun 10 2017 *)

More terms from Sascha Kurz, Jan 09 2003 and from Dean Hickerson, Jan 17 2003

A082896 a(n) = A082893(n)/n.

Original entry on oeis.org

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

Offset: 1

Labos Elemer, Apr 22 2003

nonn

Checked for the first 120000 terms to be the same as A079416. - R. J. Mathar, Sep 17 2008

Robert Israel, A079416 = A082896, Posting to Seqfan mailing list, Oct 30, 2019

Cf. A079416, A082893-A082900.

Table[Floor[(Floor[n/2]+Prime)/n], {n, 1, 100}]

a(n) = floor((floor(n/2) + p(n))/n), where p(n) is the n-th prime.

A079415 a(n) = floor(prime(n)/n) * ceiling(prime(n)/n) / 2.

Original entry on oeis.org

2, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 15, 10, 10, 10, 15, 15, 15, 15, 15, 15, 15

Offset: 1

Reinhard Zumkeller, Jan 07 2003

nonn

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

Cf. A038605, A079416, A000040.

[Floor(NthPrime(n)/n)*Ceiling(NthPrime(n)/n)/2: n in [1..80]]; // G. C. Greubel, Jan 19 2019

fc[n_]:=Module[{c=Prime[n]/n},(Floor[c]Ceiling[c])/2]; Array[fc,80] (* Harvey P. Dale, May 20 2015 *)

vector(80, n, floor(prime(n)/n)*ceil(prime(n)/n)/2) \\ G. C. Greubel, Jan 19 2019

[floor(nth_prime(n)/n)*ceil(nth_prime(n)/n)/2 for n in (1..80)] # G. C. Greubel, Jan 19 2019

cp's OEIS Frontend

A079418 Numbers k such that prime(k)/k < prime(k-1)/(k-1).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A079417 Numbers n such that round(prime(n)/n) < round(prime(n-1)/(n-1)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A082896 a(n) = A082893(n)/n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A079415 a(n) = floor(prime(n)/n) * ceiling(prime(n)/n) / 2.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage