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A045751
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Numbers k such that 4*k + 1 is not prime.
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14
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0, 2, 5, 6, 8, 11, 12, 14, 16, 17, 19, 20, 21, 23, 26, 29, 30, 31, 32, 33, 35, 36, 38, 40, 41, 42, 44, 46, 47, 50, 51, 52, 53, 54, 55, 56, 59, 61, 62, 63, 65, 66, 68, 71, 72, 74, 75, 76, 77, 80, 81, 82, 83, 85, 86, 89, 90, 91, 92, 94, 95, 96, 98, 101, 103, 104, 106, 107, 109
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OFFSET
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1,2
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COMMENTS
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Terms (except 0) can be written as 4xy +- (x+y) for x > 0, y > 0. - Ron R Spencer, Jul 28 2016
Numbers k such that (4*k)!/(4*k + 1) is an integer. - Peter Bala, Jan 25 2017
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LINKS
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EXAMPLE
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Distribution of the positive terms in the following triangular array:
2;
*, 6;
5, *, 12;
*, 11, *, 20;
8, *, 19, *, 30;
*, 16, *, 29, *, 42;
11, *, 26, *, 41, *, 56;
*, 21, *, 38, *, 55, *, 72;
14, *, 33, *, 52, *, 71, *, 90;
*, 26, *, 47, *, 68, *, 89, *, 110;
17, *, 40, *, 63, *, 86, *, 109, *, 132;
etc., where * marks the noninteger values of (2*h*k + k + h)/2 with h >= k >= 1. - Vincenzo Librandi, Jan 14 2013
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MAPLE
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for n from 0 to 100 do
if irem(factorial(4*n), 4*n+1) = 0 then print(n); end if;
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MATHEMATICA
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Select[Range[0, 200], ! PrimeQ[4 # + 1] &]
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PROG
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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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EXTENSIONS
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STATUS
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approved
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