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Search: id:A159828
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| A159828 |
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a(n) is smallest number m > 0 such that m^2+n^2+1 is prime. |
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+0
2
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| 1, 6, 1, 6, 9, 2, 3, 6, 1, 6, 3, 2, 3, 6, 1, 6, 27, 8, 9, 24, 1, 6, 21, 4, 69, 12, 3, 6, 21, 6, 3, 6, 1, 6, 9, 2, 9, 6, 1, 6, 15, 6, 9, 6, 1, 6, 27, 2, 3, 36, 9, 6, 3, 6, 15, 18, 1, 48, 3, 4, 9, 6, 7, 6, 15, 4, 21, 42, 5, 6, 3, 2, 69, 18, 5, 6, 3, 2, 9, 24, 1, 6, 3, 8, 9, 6, 11, 18, 15, 4, 3, 6, 7, 18
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(2k-1) is odd, a(2k) is even.
There are infinitely many primes of the forms n^2+m^2 and n^2+m^2+1, but it is not known if the number of primes of the form n^2+1 is infinite; cf. comments in A002496, A002313, A079544.
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EXAMPLE
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n = 1: 1^2+1^2+1 = 3 is prime, so a(1) = 1.
n = 2: 1^2+2^2+1 = 6, 2^2+2^2+1 = 9, 3^2+2^2+1 = 14, 4^2+2^2+1 = 21, 5^2+2^2+1 = 30 are composite, but 6^2+2^2+1 = 41 is prime, so a(2) = 6.
n = 27: 1^2+27^2+1 = 731 = 17*43, 2^2+27^2+1 = 734 = 2*367 are composite, but 3^2+27^2+1 = 739 is prime, so a(27) = 3.
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PROGRAM
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(MAGMA) S:=[]; for n in [1..100] do q:=n^2+1; m:=1; while not IsPrime(m^2+q) do m+:=1; end while; Append(~S, m); end for; S; [From Klaus Brockhaus, May 21 2009]
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CROSSREFS
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Cf. A069003 (smallest d such that n^2+d^2 is prime), A002496 (primes of form n^2+1), A002313 (primes of form x^2+y^2), A079544 (primes of form x^2+y^2+1, x>0, y>0).
Sequence in context: A156163 A011300 A157292 this_sequence A131114 A127778 A076714
Adjacent sequences: A159825 A159826 A159827 this_sequence A159829 A159830 A159831
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KEYWORD
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easy,nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 23 2009
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 21 2009
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