A141652 Primes of the form n/(p(n)-p(n-1)), where p(n)=n-th prime.

2, 2, 3, 2, 7, 5, 7, 17, 23, 29, 19, 41, 11, 17, 37, 41, 31, 101, 17, 53, 113, 59, 41, 127, 43, 13, 11, 139, 29, 157, 89, 61, 37, 103, 109, 113, 239, 251, 137, 101, 61, 307, 313, 337, 373, 127, 101, 137, 419, 113, 457, 461, 239, 479, 167, 103, 181, 139, 47, 193, 101, 107, 653

Offset

1,1

Comments

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

Links

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

Example

n=2: 2/(p(2)-p(2-1))=2/(3-2)=2=a(1).
n=4: 4/(p(4)-p(4-1))=4/(7-5)=2=a(2).
n=6: 6/(p(6)-p(6-1))=6/(13-11)=3=a(3).
n=12: 12/(p(12)-p(12-1))=12/(37-31)=2=a(4).
n=14: 14/(p(14)-p(14-1))=14/(43-41)=7=a(5).
n=20: 20/(p(20)-p(20-1))=20/(71-67)=5=a(6).
n=28: 28/(p(28)-p(28-1))=28/(107-103)=7=a(7),

Mathematica

Select[Table[n/(Prime[n]-Prime[n-1]), {n, 2, 2500}], PrimeQ] (* Harvey P. Dale, Jan 23 2013 *)
With[{nn=3000}, Select[#[[1]]/#[[2]]&/@Thread[{Range[2, nn], Abs[ Differences[ Prime[Range[nn]]]]}], PrimeQ]] (* Harvey P. Dale, Jun 18 2017 *)

Crossrefs

Cf. A000040.

Sequence in context: A084705 A051886 A244080 * A117754 A248577 A015999

Adjacent sequences: A141649 A141650 A141651 * A141653 A141654 A141655

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 13 2008

Extensions

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

Status

approved