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Search: id:A145823
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| A145823 |
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Squares of the form p1 - 1 where p1 is a lower twin prime. |
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+0
1
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| 4, 16, 100, 196, 5476, 8836, 16900, 17956, 21316, 25600, 52900, 65536, 106276, 115600, 122500, 164836, 184900, 193600, 220900, 341056, 401956, 470596, 490000, 495616, 614656, 739600, 846400, 972196, 1110916, 1144900, 1336336, 1464100
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These numbers are of the form 3n+1. This follows from the fact that a lower
twin prime > 3 is of the form 3n+2. If p1 = 3n+1 then the upper twin would be
3n+1+2 = 3k which is not prime for k > 1. 4 is the only square which is a
lower twin prime + 1. If a lower twin prime p1 + 1 is a square, then it is of
the form 3n+2+1 or 3n. Then 3n = x^2 implies x = 3r for some r. This implies
3n = 9r^2. Now if we subtract 1 we have 9r^2-1 = (3r-1)(3r+1) which is not
prime.
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FORMULA
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a(n) = A080149(n)^2. [From Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 24 2008]
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EXAMPLE
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p1=5 is a lower twin prime. 5-1 = 4 is a square.
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PROGRAM
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(PARI) g(n) = for(x=1, n, y=twinl(x)-1; if(issquare(y), print1(y", ")))
twinl(n) = local(c, x); c=0; x=1; while(c<n, if(ispseudoprime(prime(x)+2), c++);
x++; ); return(prime(x-1))
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CROSSREFS
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Sequence in context: A091040 A029985 A114023 this_sequence A121142 A087296 A065731
Adjacent sequences: A145820 A145821 A145822 this_sequence A145824 A145825 A145826
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Oct 20 2008
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 24 2008
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