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A152786
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Integers n such that (n^2)/2 is the arithmetic mean of a pair of twin primes.
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4
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6, 12, 42, 48, 72, 84, 90, 174, 204, 264, 306, 372, 408, 456, 474, 546, 594, 600, 642, 750, 852, 882, 936, 972, 978, 1038, 1140, 1212, 1272, 1386, 1470, 1512, 1518, 1584, 1770, 1836, 1902, 1980, 1986, 2130, 2196, 2256, 2262, 2316, 2382, 2652, 2688, 2718
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OFFSET
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1,1
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COMMENTS
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Square roots of A054735 where these are integer.
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..4288 (All terms up to 10^6.)
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FORMULA
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{n: n^2= A054735(i), any i} - R. J. Mathar, Dec 12 1008
a(n) = 6*A037073(n). [Zak Seidov, seqfan list, Aug 20 2010] [From R. J. Mathar, Sep 07 2010]
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EXAMPLE
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(6^2)/2=18= mean(17,19); (12^2)/2=72=mean(71,73); (42^2)/2=882=mean(881,883).
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MATHEMATICA
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lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; If[p2-p1==2, e=(2*(p1+1))^(1/2); i=Floor[e]; If[e==i, AppendTo[lst, i]]], {n, 3*9!}]; lst
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PROG
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(PARI) forstep(n=6, 1e3, 6, if(isprime(n^2/2-1)&&isprime(n^2/2+1), print1(n", "))) \\ Charles R Greathouse IV, Feb 01 2013
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CROSSREFS
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A152786 = 6*A037073. - Zak Seidov, Aug 20 2010
Cf. A014574, A152788 (cubic version).
Subsequence of A074924. - Zak Seidov, Feb 01 2013
Sequence in context: A185616 A052747 A007121 * A206039 A048069 A152787
Adjacent sequences: A152783 A152784 A152785 * A152787 A152788 A152789
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KEYWORD
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nonn
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, Dec 12 2008
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EXTENSIONS
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Edited by R. J. Mathar, Dec 12 2008
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STATUS
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approved
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