A141637 Primes of the form n/(p(n+1)-p(n)), where p(n)=n-th prime.

2, 5, 3, 3, 3, 13, 11, 17, 71, 29, 89, 103, 61, 31, 131, 151, 31, 173, 59, 199, 71, 31, 73, 229, 61, 271, 293, 151, 101, 103, 89, 181, 127, 197, 397, 137, 103, 431, 439, 149, 467, 131, 263, 181, 283, 293, 599, 619, 317, 367, 769, 257, 197, 263, 809, 271, 821, 167, 61, 433, 179, 449

Offset

1,1

Comments

Entries may be repeated and are shown in order of increasing generator n.

Links

Table of n, a(n) for n=1..62.

Example

n=8: 8/(p(8+1)-p(8))=8/(23-19)=2=a(1).
n=10: 10/(p(10+1)-p(10))=10/(31-29)=5=a(2).
n=12: 12/(p(12+1)-p(12))=12/(41-37)=3=a(3).
n=18: 18/(p(18+1)-p(18))=18/(67-61)=3=a(4).
n=24: 24/(p(24+1)-p(24))=24/(97-89)=3=a(5).
n=26: 26/(p(26+1)-p(26))=26/(103-101)=13=a(6),

Mathematica

With[{nn=3000}, Select[#[[1]]/#[[2]]&/@Thread[{Range[nn-1], #[[2]]-#[[1]]&/@ Partition[Prime[Range[nn]], 2, 1]}], PrimeQ]] (* Harvey P. Dale, Apr 13 2015 *)

Crossrefs

Cf. A000040.

Sequence in context: A004200 A069998 A162405 * A185581 A151960 A281300

Adjacent sequences: A141634 A141635 A141636 * A141638 A141639 A141640

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 12 2008

Extensions

Corrected and extended by R. J. Mathar, Sep 26 2008

Status

approved