A107471 a(n) = 3*prime(n) - 2*prime(n+1).

0, -1, 1, -1, 7, 5, 13, 11, 11, 25, 19, 29, 37, 35, 35, 41, 55, 49, 59, 67, 61, 71, 71, 73, 89, 97, 95, 103, 101, 85, 119, 119, 133, 119, 145, 139, 145, 155, 155, 161, 175, 161, 187, 185, 193, 175, 187, 215, 223, 221, 221, 235, 221, 239, 245, 251, 265, 259, 269, 277, 263, 265, 299, 307, 305, 289, 319, 317, 343, 341, 341

Offset

1,5

Comments

a(n) > 0 for n >= 5. For 5 <= n <= 24 can be shown by observation. For n > 24, Jitsuro Nagura proved that for some integer k, there is always a prime between k and (6/5)*k. Therefore 3*prime(n) - 2*prime(n+1) >= (3/5)*prime(n) > 0. - Ryan Bresler, Nov 17 2021

Links

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

Jitsuro Nagura, On the interval containing at least one prime number, Proc. Japan Acad., 28 (1952), 177-181.

Example

a(5)=7 because prime(5)=11, prime(6)=13 and 3*11 - 2*13 = 7.

Maple

a:=n->3*ithprime(n)-2*ithprime(n+1): seq(a(n), n=1..80); # Emeric Deutsch, May 28 2005

Mathematica

3#[[1]]-2#[[2]]&/@Partition[Prime[Range[80]], 2, 1] (* Harvey P. Dale, Apr 17 2017 *)

Prog

(PARI) a(n) = my(p=prime(n)); 3*p - 2*nextprime(p+1); \\ Michel Marcus, Nov 17 2021

Crossrefs

Cf. A000040.

Sequence in context: A369797 A070408 A176672 * A332768 A107323 A265794

Adjacent sequences: A107468 A107469 A107470 * A107472 A107473 A107474

Keyword

sign

Author

Leroy Quet, May 27 2005

Extensions

More terms from Emeric Deutsch, May 28 2005

Status

approved