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!)
A184417 p^2 + (p+2)^2 - 1 where (p,p+2) is the n-th twin prime pair. 1
33, 73, 289, 649, 1801, 3529, 7201, 10369, 20809, 23329, 38089, 45001, 64801, 73729, 78409, 103969, 115201, 145801, 159049, 194689, 242209, 352801, 373249, 426889, 544969, 649801, 720001, 763849, 824329, 871201, 1312201, 1351369, 1371169, 1472329, 1555849, 2080801, 2130049, 2205001, 2255689, 2384929, 2654209 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This seems to have a disproportionately high probability of generating a prime number.
LINKS
FORMULA
a(n) = A063533(n) - 1.
EXAMPLE
a(1) = prime(1)^2 + (prime(1)+2)^2 - 1 = 3^2 + (3+2)^2 - 1 = 33;
a(2) = prime(2)^2 + (prime(2)+2)^2 - 1 = 5^2 + (5+2)^2 - 1 = 73;
a(3) = prime(3)^2 + (prime(3)+2)^2 - 1 = 11^2 + (11+2)^2 - 1 = 289.
MATHEMATICA
Total/@(Select[Partition[Prime[Range[500]], 2, 1], #[[2]]-#[[1]]==2&]^2)-1 (* Harvey P. Dale, Feb 24 2011 *)
CROSSREFS
Sequence in context: A015722 A103046 A063868 * A240884 A049012 A137187
KEYWORD
nonn
AUTHOR
Robert Mohr, Feb 13 2011
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 03:43 EDT 2024. Contains 372618 sequences. (Running on oeis4.)