A141633 Primes of the form j-(p(j+3)-p(j))/(p(j+2)-p(j+1)), where p(j)=j-th prime.

2, 3, 7, 13, 17, 19, 23, 29, 31, 41, 43, 59, 61, 67, 73, 83, 101, 103, 107, 109, 113, 127, 163, 167, 179, 193, 199, 223, 233, 239, 241, 257, 281, 307, 311, 353, 373, 401, 409, 419, 443, 449, 461, 463, 487, 491, 499, 523, 541, 547, 569, 599, 607, 613, 659, 661, 677, 701, 709

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 10 2008

Keywords

• nonn
• less

Comments

Primes of the form j-A031165(j)/A001223(j+1). In cases like j=28 and j=32 which create the same prime (here: 23), the prime is only listed once.

Examples

			If j=12, then 12-(p(12+3)-p(12))/(p(12+2)-p(12+1))=12-(47-37)/(43-41)=7=a(3).
If j=48, then 48-(p(48+3)-p(48))/(p(48+2)-p(48+1))=48-(233-223)/(229-227)=43: prime, in the sequence.
If j=88, then 88-(p(88+3)-p(88))/(p(88+2)-p(88+1))=88-(467-457)/(463-461)=83: prime, in the sequence
		

Crossrefs

Cf. A000040.

Programs

Mathematica

Select[Table[n-(Prime[n+3]-Prime[n])/(Prime[n+2]-Prime[n+1]),{n,1000}],PrimeQ[ #] &&#>0&]//Union (* Harvey P. Dale, Aug 12 2020 *)

Extensions

Corrected definition and examples, added many more terms - R. J. Mathar, Sep 13 2008