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!)
A154672 Numbers n = 5*k^2 such that n - 1 and n + 1 are (twin) primes (thus k=6*m). 6
180, 1620, 8820, 35280, 87120, 151380, 302580, 380880, 691920, 737280, 808020, 1393920, 5020020, 5767380, 7712820, 9604980, 10281780, 11160180, 12450420, 12736080, 14723280, 15138000, 17186580, 17860500, 18663120, 18779220, 19129680, 21300480 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Original definition: Averages of twin prime pairs n such that n*5 and n/5 are squares.
Obviously, n*5 is a square iff n/5 is a square, say k^2. But n=5k^2 can't be the average of a twin prime pair unless it's a multiple of 6, thus k=6m and n=5*36*m^2. - M. F. Hasler, Apr 11 2009
LINKS
FORMULA
A154672 = 5*A000290 intersect A014574 = 180*A000290 intersect A014574. - M. F. Hasler, Apr 11 2009
MATHEMATICA
lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1], s=(n*5)^(1/2); If[Floor[s]==s, AppendTo[lst, n]]], {n, 6, 10!, 6}]; lst (*...and/or...*) lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1], s=(n/5)^(1/2); If[Floor[s]==s, AppendTo[lst, n]]], {n, 6, 10!, 6}]; lst
PROG
(PARI) forstep(k=0, 1e4, 6, isprime(k^2*5+1) & isprime(k^2*5-1) & print1(k^2*5, ", ")) \\ M. F. Hasler, Apr 11 2009
CROSSREFS
Sequence in context: A225932 A081380 A115184 * A211556 A364162 A184225
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited and extended by M. F. Hasler, Apr 11 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 June 18 13:40 EDT 2024. Contains 373481 sequences. (Running on oeis4.)