A141578 Primes of the form n-(p(n+2)-p(n))/(p(n+1)-p(n-1)), where p(n)=n-th prime.

3, 5, 29, 37, 41, 43, 59, 71, 103, 103, 149, 151, 149, 181, 191, 211, 211, 263, 271, 271, 313, 313, 331, 347, 347, 349, 383, 389, 397, 433, 521, 523, 577, 607, 709, 743, 743, 769, 787, 787, 821, 823, 827, 829, 863, 877, 877, 883, 937, 1039, 1061, 1069, 1117, 1129, 1153

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=4: 4-(13-7)/(11-5)=3=a(1).
n=6: 6-(19-13)/(17-11)=5=a(2).
n=30: 30-(131-113)/(127-109)=29=a(3).
n=38: 38-(173-163)/(167-157)=37=a(4).
n=42: 42-(193-181)/(191-179)=41=a(5).

Mathematica

With[{nn=2000}, Select[#[[1]]-#[[2]]&/@(Thread[{Range[2, nn-2], (#[[4]]- #[[2]])/ (#[[3]]-#[[1]])&/@Partition[Prime[Range[nn]], 4, 1]}]), PrimeQ]] (* Harvey P. Dale, Sep 12 2017 *)

Crossrefs

Cf. A000040.

Sequence in context: A321069 A355273 A361085 * A327748 A272345 A356147

Adjacent sequences: A141575 A141576 A141577 * A141579 A141580 A141581

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 10 2008

Extensions

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

Status

approved