The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A145824 Lower twin primes p1 such that p1-1 is a square. 3
 5, 17, 101, 197, 5477, 8837, 16901, 17957, 21317, 25601, 52901, 65537, 106277, 115601, 122501, 164837, 184901, 193601, 220901, 341057, 401957, 470597, 490001, 495617, 614657, 739601, 846401, 972197, 1110917, 1144901, 1336337, 1464101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 3 is the only lower twin prime for which p1+1 is a square. This follows from the fact that lower twin primes > 3 are of the form 3n+2 and adding 1 we get a number of the form 3m. Then 3m = k^2 implies k = 3r and 3m = 9r^2. Subtracting 1 we have 3m = (3r-1)(3r+1) not prime contradicting 3m-1 is prime. Conjecture: There exist an infinite number of primes of this form. a(n) = A080149(n)^2 + 1. - Zak Seidov, Oct 21 2008 LINKS Zak Seidov, Table of n, a(n) for n=1..4663, a(n)<10^12 EXAMPLE p1 = 5 is a lower twin prime. 5-1 = 4 is a square. MATHEMATICA lst={}; Do[p=Prime@n; If[PrimeQ@(p+2)&&Sqrt[p-1]==IntegerPart[Sqrt[p-1]], AppendTo[lst, p]], {n, 9!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 11 2009 *) PROG (PARI) g(n) = for(x=1, n, y=twinl(x)-1; if(issquare(y), print1(y+1", "))) twinl(n) = local(c, x); c=0; x=1; while(c

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 December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)