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A154676
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Numbers n = 103*k^2 such that (n-1,n+1) is a twin prime pair (thus k = 6*m).
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6
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2317500, 12047292, 26163648, 43250112, 47347452, 61704828, 168228252, 333720000, 351755712, 426127068, 513127872, 840143808, 979638768, 998790588, 1089276912, 1330434108, 1357220700, 1388809152, 1694467008, 1927570428, 1986835392, 2035992348, 2136108348, 2858437872, 3070594800, 3241626300, 3903322608
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OFFSET
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1,1
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COMMENTS
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Original definition: Averages of twin prime pairs n such that n*103 and n/103 are squares.
All terms are of the form 3708*k^2. - Zak Seidov, Jan 15 2009
Obviously n*103 is a square iff n/103 is a square, say k^2. But n=103k^2 can't be the average of a twin prime pair unless it's a multiple of 6, thus k=6m and n=103*36*m^2. - M. F. Hasler, Apr 11 2009
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LINKS
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MAPLE
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select(t -> isprime(t+1) and isprime(t-1), [seq(3708*i^2, i=1..2000)]); # Robert Israel, Mar 13 2019
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MATHEMATICA
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lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1], s=(n*103)^(1/2); If[Floor[s]==s, AppendTo[lst, n]]], {n, 9!, 2*11!, 6}]; lst (*...and/or...*) lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1], s=(n/103)^(1/2); If[Floor[s]==s, AppendTo[lst, n]]], {n, 9!, 2*11!, 6}]; lst
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PROG
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(PARI) forstep(k=0, 1e4, 6, isprime(k^2*103+1) & isprime(k^2*103-1) & print1(k^2*103, ", ")) \\ M. F. Hasler, Apr 11 2009
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CROSSREFS
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KEYWORD
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nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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