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A121326
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Primes of the form 4*n^2 + 1.
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9
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5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857, 41617, 42437, 44101, 50177, 52901, 55697
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Except for the initial 2 in A002496 this sequence is the same as A002496. Conjecture: The prime factors of all numbers of the form 4n^2+1 are also of the form 4m+1.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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EXAMPLE
| For n=4, 4n^2+1 = 17, prime.
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MATHEMATICA
| lst={}; Do[p=4*n^2+1; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 28 2009]
Select[Table[4n^2+1, {n, 0, 800}], PrimeQ] (* Vincenzo Librandi, Dec 02 2011 *)
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PROG
| (PARI) for(x=1, 200, y=4*x^2+1; if(isprime(y), print1(y", ")))
(MAGMA) [a: n in [0..400] | IsPrime(a) where a is 4*n^2+1]; // Vincenzo Librandi, Dec 02 2011
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CROSSREFS
| Cf. A002496.
Sequence in context: A145012 A147204 A168024 * A147219 A146280 A147181
Adjacent sequences: A121323 A121324 A121325 * A121327 A121328 A121329
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KEYWORD
| nonn,easy
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Aug 26 2006
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