A079419 -id:A079419 - 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

A358530 a(n) = n-th prime prime(k) such that prime(k) - prime(k-1) < prime(k-1) - prime(k-2).

Original entry on oeis.org

13, 19, 31, 41, 43, 61, 71, 73, 83, 101, 103, 109, 131, 139, 151, 167, 181, 193, 199, 227, 229, 241, 257, 271, 281, 283, 311, 313, 337, 349, 373, 383, 401, 421, 433, 443, 461, 463, 487, 491, 503, 523, 547, 563, 571, 593, 601, 617, 619, 641, 643, 661, 677

Offset: 1

Clark Kimberling, Nov 21 2022

This sequence, together with A358528 and A181424, partition the set of primes >= 5. The corresponding sequences of indices, A358531, A358529, and A356347, partition the set of positive integers >= 3.

			  n           1   2   3   4   5   6   7
  k           6   8  11  13  14  18  20
  prime(n)   13  19  31  41  43  61  71

Cf. A001223, A051634, A079419, A358528, A358529, A358531, A181424, A356347.

t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] < Prime[# - 1] - Prime[# - 2] &]  (* A358531 *)
Prime[t]  (* A358530 *)

a(n) = A151800(A051634(n)). - Andrew Howroyd, Sep 21 2024

Incorrect formula removed by Georg Fischer, Sep 21 2024

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