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A037073
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Numbers k such that (6*k)^2 is the sum of a twin prime pair.
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14
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1, 2, 7, 8, 12, 14, 15, 29, 34, 44, 51, 62, 68, 76, 79, 91, 99, 100, 107, 125, 142, 147, 156, 162, 163, 173, 190, 202, 212, 231, 245, 252, 253, 264, 295, 306, 317, 330, 331, 355, 366, 376, 377, 386, 397, 442, 448, 453, 462, 469, 481, 491, 498, 502, 516, 547
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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E.g. n=44 -> (6*44)^2 = 69696 = 34847 + 34849 (twin prime pair).
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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)/6, %); # Peter Luschny, Jan 05 2020
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MATHEMATICA
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Select[Sqrt[Plus@@@Select[Partition[Prime[Range[4*10^5]], 2, 1], Differences[#]=={2} &]/36], IntegerQ] (* Jayanta Basu, May 26 2013 *)
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PROG
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(PARI) is(n)=isprime(18*n^2-1)&&isprime(18*n^2+1) \\ M. F. Hasler, Oct 30 2023
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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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