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Search: id:A027862
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| A027862 |
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Primes of the form n^2 + (n+1)^2; or, primes of the form (n^2+1)/2. |
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+0
12
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| 5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613, 4513, 5101, 7321, 8581, 9661, 9941, 10513, 12641, 13613, 14281, 14621, 15313, 16381, 19013, 19801, 20201, 21013, 21841, 23981, 24421, 26681
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also, primes of the form 4n+1 which are the hypotenuse of one and only one right triangle with integral arms. - Cino Hilliard (hillcino368(AT)gmail.com), Mar 16 2003
Centered square primes (i.e. prime terms of centered squares A001844). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 21 2005
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REFERENCES
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D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc. Boston, MA, 1976, p. 271.
Morris Kline, Mathematical Thought from Ancient to Modern Times, 1972. pp. 275.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
P. De Geest, World!Of Numbers
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MATHEMATICA
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lst={}; Do[If[PrimeQ[p=n^2+(n+1)^2], (*Print[p]; *)AppendTo[lst, p]], {n, 10^3}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 21 2008]
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PROGRAM
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(PARI) je=[]; for(n=1, 500, if(isprime(n^2+(n+1)^2), je=concat(je, n^2+(n+1)^2))); je
(PARI) fermat(n) = { for(x=1, n, y=2*x*(x+1)+1; if(isprime(y), print1(y" ")) ) }
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CROSSREFS
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Primes p such that A079887(p)=1
Primes arising in A002731, A027861, A091277 gives prime index.
Sequence in context: A025490 A087938 A103729 this_sequence A100210 A080267 A034735
Adjacent sequences: A027859 A027860 A027861 this_sequence A027863 A027864 A027865
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com)
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EXTENSIONS
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More terms from Cino Hilliard (hillcino368(AT)gmail.com), Mar 16 2003
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