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Search: id:A028871
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| A028871 |
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Primes of form n^2 - 2. |
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+0
24
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| 2, 7, 23, 47, 79, 167, 223, 359, 439, 727, 839, 1087, 1223, 1367, 1847, 2207, 2399, 3023, 3719, 3967, 4759, 5039, 5623, 5927, 7919, 8647, 10607, 11447, 13687, 14159, 14639, 16127, 17159, 18223, 19319, 21023, 24023, 25919, 28559, 29927
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Except for the initial term, primes equal to the product of two consecutive even numbers minus 1. - Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Sep 24 2004
With exception first term 2 primes p such that continued fraction of (1+Sqrt[p]/2 have period 4. [From Artur Jasinski (grafix(AT)csl.pl), Feb 03 2010]
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REFERENCES
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D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.
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LINKS
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P. De Geest, Palindromic Quasipronics of the form n(n+x)
Eric Weisstein's World of Mathematics, Near-Square Prime
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EXAMPLE
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a(3) = 23, 6^2 - 2*6 - 1 = 23
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MATHEMATICA
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lst={}; Do[s=n^2; If[PrimeQ[p=s-2], AppendTo[lst, p]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 26 2008]
aa = {}; Do[If[4 == Length[ContinuedFraction[(1 + Sqrt[Prime[m]])/2][[2]]], AppendTo[aa, Prime[m]]], {m, 1, 1000}]; aa (*Artur Jasinski*) [From Artur Jasinski (grafix(AT)csl.pl), Feb 03 2010]
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CROSSREFS
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Cf. A028870.
Sequence in context: A049552 A049572 A094786 this_sequence A053705 A049001 A049002
Adjacent sequences: A028868 A028869 A028870 this_sequence A028872 A028873 A028874
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KEYWORD
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nonn,new
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com)
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