A079419 -id:A079419

Search: a079419 -id:a079419

Displaying 1-2 of 2 results found.

page 1

A079418

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

+10
5

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

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

CROSSREFS

Cf. A079417, A079416, A000040.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 07 2003

STATUS

approved

A358530

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

+10
5

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..53.

FORMULA

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

EXAMPLE

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

MATHEMATICA

t = Select[2 + Range[140],

Prime[#] - Prime[# - 1] < Prime[# - 1] - Prime[# - 2] &] (* A358531 *)

Prime[t] (* A358530 *)

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 21 2022

EXTENSIONS

Incorrect formula removed by Georg Fischer, Sep 21 2024

STATUS

approved

page 1

Search completed in 0.009 seconds