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A027861 Numbers n such that n^2 + (n+1)^2 is prime. 34
1, 2, 4, 5, 7, 9, 12, 14, 17, 19, 22, 24, 25, 29, 30, 32, 34, 35, 39, 42, 47, 50, 60, 65, 69, 70, 72, 79, 82, 84, 85, 87, 90, 97, 99, 100, 102, 104, 109, 110, 115, 122, 130, 135, 137, 139, 144, 149, 154, 157, 160, 162, 164, 167, 172, 174, 185, 187, 189, 195, 199, 202 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

n > 1 never ends in 1, 3, 6 or 8, (that is, n*(n+1) does not end in 2). - Lekraj Beedassy, Jul 09 2004

n can never be congruent to (1 or 3) mod 5. Because if it were then n^2 + (n+1)^2 would be divisible by 5. In other words for n > 1, this sequence cannot contain any values in A047219. This means that we can immediately discard 40% of all possible n. - Dmitry Kamenetsky, Sep 02 2008

LINKS

T. D. Noe and Zak Seidov, Table of n, a(n) for n = 1..10000

P. De Geest, World!Of Numbers

FORMULA

a(n) = (1/2)*(sqrt(2*A027862(n)-1)-1). - Zak Seidov, Jul 22 2013

A010051(A001844(a(n))). - Reinhard Zumkeller, Jul 13 2014

MATHEMATICA

lst={}; Do[If[PrimeQ[n^2+(n+1)^2], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

PROG

(MAGMA) [n: n in [0..1000] |IsPrime(n^2 + (n+1)^2)]; // Vincenzo Librandi, Nov 19 2010

(Haskell)

a027861 n = a027861_list !! (n-1)

a027861_list = filter ((== 1) . a010051 . a001844) [0..]

-- Reinhard Zumkeller, Jul 13 2014

(PARI) is(n)=isprime(n^2 + (n+1)^2) \\ Charles R Greathouse IV, Apr 28 2015

CROSSREFS

Complement of A012132.

Equals (A002731(n+1)-1)/2. A027862 gives primes, A091277 gives prime index.

Cf. A047219, A001844, A010051.

Sequence in context: A000788 A053039 A214051 * A219648 A062428 A250000

Adjacent sequences:  A027858 A027859 A027860 * A027862 A027863 A027864

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified April 27 06:52 EDT 2017. Contains 285508 sequences.