The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A163420 Primes p such that p+(p^2-1)/4 is also prime. 11
3, 5, 7, 11, 17, 19, 29, 31, 37, 41, 47, 59, 61, 89, 107, 109, 127, 131, 139, 151, 191, 199, 227, 229, 239, 251, 281, 307, 317, 337, 347, 359, 367, 389, 397, 439, 449, 461, 479, 487, 491, 569, 587, 601, 617, 659, 661, 677, 701, 719, 727, 769, 809, 839, 911, 941 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
A163419(n) = a(n)+( a(n)^2-1 )/4. [R. J. Mathar, Aug 17 2009]
{A000040(k): A000040(k)+A024701(k-1) in A000040}.
EXAMPLE
3 is in the sequence because 3+(3^2-1)/4=5 is a prime number.
5 is in the sequence because 5+(5^2-1)/4=11 is a prime number.
MATHEMATICA
f[n_]:=((p+1)/2)^2+((p-1)/2); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 6!}]; lst
Select[Range[700], PrimeQ[#] && PrimeQ[# + (#^2 - 1)/4] &] (* Vincenzo Librandi, Apr 08 2013 *)
Select[Prime[Range[200]], PrimeQ[#+(#^2-1)/4]&] (* Harvey P. Dale, Jun 18 2014 *)
PROG
(Magma) [p: p in PrimesInInterval(3, 1000) | IsPrime(p+(p^2-1) div 4)]; // Vincenzo Librandi, Apr 08 2013
CROSSREFS
Sequence in context: A342692 A048184 A290283 * A155489 A194099 A045396
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Definition simplified by R. J. Mathar, Aug 17 2009
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)