This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A045637 Primes of the form p^2 + 4, where p is prime. 20
 13, 29, 53, 173, 293, 1373, 2213, 4493, 5333, 9413, 10613, 18773, 26573, 27893, 37253, 54293, 76733, 85853, 94253, 97973, 100493, 120413, 139133, 214373, 237173, 253013, 299213, 332933, 351653, 368453, 375773, 458333, 552053, 619373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These are the only primes that are the sum of two primes squared. 11 = 3^2 + 2 is the only prime of the form p^2 + 2 because all primes greater than 3 can be written as p=6n-1 or p=6n+1, which allows p^2+2 to be factored. - T. D. Noe, May 18 2007 Infinite under the Bunyakovsky conjecture. - Charles R Greathouse IV, Jul 04 2011 All terms > 29 are congruent to 53 mod 120. - Zak Seidov, Nov 06 2013 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A062324(n)^2 + 4. - Zak Seidov, Nov 06 2013 EXAMPLE 29 belongs to the sequence because it equals 5^2 + 4. MATHEMATICA Select[Prime[ # ]^2+4&/@Range[140], PrimeQ] PROG (PARI) forprime(p=2, 1e4, if(isprime(t=p^2+4), print1(t", "))) \\ Charles R Greathouse IV, Jul 04 2011 CROSSREFS The corresponding primes p are in A062324. Subsequence of A005473 (and thus A185086). Cf. A094473-A094479. Sequence in context: A090866 A098062 A094481 * A146743 A065546 A075636 Adjacent sequences:  A045634 A045635 A045636 * A045638 A045639 A045640 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by Dean Hickerson, Dec 10 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 06:03 EDT 2018. Contains 316405 sequences. (Running on oeis4.)