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A282057
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Odd numbers n such that for all k >= 1 the numbers n*4^k - 1 and n*4^k + 1 do not form a twin prime pair.
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0
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5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 29, 31, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 89, 91, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 119, 121
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OFFSET
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1,1
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COMMENTS
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Next term is 123 or 125.
A sufficient condition for an odd number > 1 to belong to this sequence is that it not be congruent to 3, 15 or 27 mod 30.
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LINKS
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EXAMPLE
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3 is not in the sequence because 3*4^1 - 1 = 11 and 3*4^1 + 1 = 13 are a pair of twin primes.
5 is in the sequence because gcd(5 + 1, 4 - 1) = 3 is a trivial factor of 5*4^k + 1. Therefore, for all k >= 1 the numbers 5*4^k - 1 and 5*4^k + 1 do not form a twin prime pair.
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PROG
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(Magma) lst:=[]; for n in [3..121 by 2] do if not n mod 30 in {3, 15, 27} then Append(~lst, n); else k:=1; while not IsPrime(n*4^k+1) or not IsPrime(n*4^k-1) do k+:=1; end while; end if; end for; lst;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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