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A027861
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Numbers n such that n^2 + (n+1)^2 is prime.
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16
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| n>1 never ends in 1, 3, 6 or 8, (i.e. n*(n+1) does not end in 2). - Lekraj Beedassy (blekraj(AT)yahoo.com), 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 (dkamen(AT)rsise.anu.edu.au), Sep 02 2008
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
P. De Geest, World!Of Numbers
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MATHEMATICA
| lst={}; Do[If[PrimeQ[n^2+(n+1)^2], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 21 2008]
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PROG
| (MAGMA) [n: n in [0..1000] |IsPrime(n^2 + (n+1)^2)] [From V. Librandi, Nov 19 2010]
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CROSSREFS
| Complement of A012132 - Michael Somos, Jun 08, 2000.
Equals (A002731(n+1)-1)/2. A027862 gives primes, A091277 gives prime index.
Cf. A047219.
Sequence in context: A158618 A000788 A053039 * A062428 A056833 A105771
Adjacent sequences: A027858 A027859 A027860 * A027862 A027863 A027864
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KEYWORD
| nonn,easy
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com)
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