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A027861
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Numbers k such that k^2 + (k+1)^2 is prime.
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38
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1, 2, 4, 5, 7, 9, 12, 14, 17, 19, 22, 24, 25, 29, 30, 32, 34, 35, 39, 42, 47, 50, 60, 65, 69, 70, 72, 79, 82, 84, 85, 87, 90, 97, 99, 100, 102, 104, 109, 110, 115, 122, 130, 135, 137, 139, 144, 149, 154, 157, 160, 162, 164, 167, 172, 174, 185, 187, 189, 195, 199, 202
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OFFSET
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1,2
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COMMENTS
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k > 1 never ends in 1, 3, 6 or 8, (that is, k*(k+1) does not end in 2). - Lekraj Beedassy, Jul 09 2004
k can never be congruent to (1 or 3) mod 5, because if it were, then k^2 + (k+1)^2 would be divisible by 5. In other words, for k > 1, this sequence cannot contain any values in A047219. This means that we can immediately discard 40% of all possible k. - Dmitry Kamenetsky, Sep 02 2008
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[250], PrimeQ[#^2+(#+1)^2]&] (* Harvey P. Dale, Dec 31 2017 *)
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PROG
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(Magma) [n: n in [0..1000] |IsPrime(n^2 + (n+1)^2)]; // Vincenzo Librandi, Nov 19 2010
(Haskell)
a027861 n = a027861_list !! (n-1)
a027861_list = filter ((== 1) . a010051 . a001844) [0..]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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