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A152786
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Integers k such that (k^2)/2 is the arithmetic mean of a pair of twin primes.
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6
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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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FORMULA
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EXAMPLE
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6 is a term since (6^2)/2 = 18 = mean(17, 19).
12 is a term since (12^2)/2 = 72 = mean(71,73).
42 is a term since (42^2)/2 = 882 = mean(881,883).
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MAPLE
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isa := n -> isprime(n) and isprime(n+2) and issqr(2*n+2):
select(isa, [$4..1000000]): map(n -> sqrt(2*n+2), %); # Peter Luschny, Jan 05 2020
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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
(* Second program: *)
Select[Map[Sqrt[2 #] &, Mean /@ Select[Partition[Prime@ Range[10^6], 2, 1], Subtract @@ # == -2 &]], IntegerQ] (* Michael De Vlieger, Feb 18 2018 *)
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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
(Magma) [k:k in [2..2800 by 2]| IsPrime(k*k div 2 -1) and IsPrime(k*k div 2 +1)]; // Marius A. Burtea, Jan 01 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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