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!)
A224888 Primes of the form p^2 + (q-p)^2, where p and q are consecutive primes. 2
5, 13, 29, 293, 997, 6257, 11897, 18773, 19421, 52457, 73477, 109597, 120413, 167381, 192737, 218233, 249017, 292717, 333029, 361237, 398261, 466553, 502781, 546137, 552113, 591377, 635353, 683933, 687341, 704117, 737897, 885517, 966353, 982117, 1018097, 1079621 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Primes of the form A000040(n)^2 + A001223(n)^2.
Primes of the form A134735(2n-1)^2 + A134735(2n)^2.
Conjecture: a(n) ~ A093343(n).
There are 20421247 members of this sequence below 10^20. - Charles R Greathouse IV, Jul 29 2013
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
c(x) is O( sqrt(x/log x) / log x ), where c(x) is the counting function, the number of terms less than x.
EXAMPLE
3 and 5 are consecutive primes and 3^2 + (5-3)^2 = 9 + 4 = 13 is prime, so 13 is in the sequence.
MATHEMATICA
Select[Table[Prime[n]^2 + (Prime[n + 1] - Prime[n])^2, {n, 200}], PrimeQ] (* Alonso del Arte, Jul 29 2013 *)
PROG
(PARI) p=2; forprime(q=3, 1e4, if(isprime(t=p^2+(q-p)^2), print1(t", ")); p=q) \\ Charles R Greathouse IV, Jul 24 2013
CROSSREFS
Cf. A093343.
Sequence in context: A147492 A182069 A085555 * A256314 A002768 A354292
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Jul 24 2013
EXTENSIONS
a(5), a(9)-a(36) from Charles R Greathouse IV, Jul 24 2013
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 March 4 12:45 EST 2024. Contains 370532 sequences. (Running on oeis4.)