The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A231017 Least prime q > p = prime(n) such that if d = q-p, then p, p+d, p+2d, ..., p+(p-1)d are all primes. 3
 3, 5, 11, 157, 1536160091, 9918821194603, 341976204789992332577, 2166703103992332274919569 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Second term in the smallest non-constant p-term arithmetic progression (AP) of primes beginning with p = prime(n). For any non-constant AP beginning with a prime p and ending with a prime, the maximum possible length is p, since p+pd is not prime for d > 0. If all the terms are prime, then the common difference d must be a multiple of all primes < p. Ribenboim says that in 1986 G. Loh [Loeh] discovered a(5) and a(6), and that a(n) should exist for all n, but "in my opinion, this is so difficult that no one will prove [it], and no one will find a counterexample in the near future." Phil Carmody found a(7) in 2001. See the crossrefs for more comments, references, and links. REFERENCES P. Ribenboim, My Numbers, My Friends, Springer, 2000; p. 67. P. Ribenboim, The Book of Prime Number Records, 2nd ed., Springer, 1989; p. 225. LINKS Phil Carmody, a(7), NMBRTHRY November 2001. FORMULA a(n) = prime(n) + A088430(n) = prime(n) + A002110(n)*A231018(n). EXAMPLE Prime(3) = 5 and 5, 11, 17, 23, 29 is the smallest 5-term AP beginning with 5, so a(3) = 11. PROG (PARI) a(n)=my(p=prime(n), P=prod(i=1, n-1, prime(i)), d); forprime(q=p+1, , d=q-p; if(d%P, next); for(i=2, p-1, if(!isprime(p+i*d), next(2))); return(q)) \\ Charles R Greathouse IV, Nov 08 2013 CROSSREFS For common differences see A088430, for initial terms see A000040, for last terms see A113834, for the APs see A231406. For other types of APs of primes see A005115 and its comments. Sequence in context: A277552 A154941 A062601 * A038198 A280876 A079037 Adjacent sequences:  A231014 A231015 A231016 * A231018 A231019 A231020 KEYWORD hard,more,nonn AUTHOR Jonathan Sondow, Nov 08 2013 EXTENSIONS a(8) found by Wojciech Izykowski, from Jens Kruse Andersen, Jun 30 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 21 18:55 EDT 2022. Contains 353926 sequences. (Running on oeis4.)