The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A090698 Primes of the form 2*n^2+1. 13
 3, 19, 73, 163, 883, 1153, 1459, 1801, 2179, 2593, 3529, 4051, 8713, 10369, 11251, 15139, 17299, 18433, 19603, 20809, 22051, 30259, 34849, 36451, 46819, 48673, 52489, 62659, 69193, 71443, 80803, 83233, 95923, 103969, 112339, 115201, 130051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A prime p can be expressed as either the sum of two squares or the sum of two squares - 1, p = X^2 + Y^2 or p = X^2 + Y^2 - 1, if and only if p is of the form 2*(m^2)+1 where m is either 1 or a multiple of 3. Conjecture: 2^(a(n)-1) - 3 is not prime. - Vincenzo Librandi, Feb 04 2013. Primes in A058331. - Vincenzo Librandi, Apr 10 2015 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..5000 FORMULA a(n)=2*A089001(n)^2+1 = A000040(A090612(n)). EXAMPLE 19 = 2^2 + 4^2 - 1 = 2*(3^2)+1 73 = 5^2 + 7^2 - 1 = 2*(6^2)+1 163= 8^2 + 10^2 -1 = 2*(9^2)+1 883= 10^2+ 28^2 -1 = 2*(21^2)+1 MATHEMATICA Select[Table[2n^2+1, {n, 0, 900}], PrimeQ] (* Vincenzo Librandi, Dec 02 2011 *) PROG (Magma)[a: n in [0..400] | IsPrime(a) where a is 2*n^2+1]; // Vincenzo Librandi, Dec 02 2011 (PARI) is(n)=isprime(2*n^2+1) \\ Charles R Greathouse IV, Jan 05 2013 CROSSREFS Cf. A058331, A089001, A089008, A090612. Sequence in context: A059599 A183461 A095662 * A350713 A215802 A202041 Adjacent sequences: A090695 A090696 A090697 * A090699 A090700 A090701 KEYWORD nonn,easy AUTHOR Kurmang. Aziz. Rashid, Dec 20 2003 EXTENSIONS Extended by Ray Chandler, Dec 21 2003 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.

Last modified December 1 21:21 EST 2023. Contains 367502 sequences. (Running on oeis4.)