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A090612
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Numbers k such that the k-th prime is of the form 2*j^2 + 1.
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5
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2, 8, 21, 38, 153, 191, 232, 279, 327, 378, 493, 559, 1086, 1272, 1360, 1769, 1989, 2111, 2224, 2344, 2471, 3272, 3721, 3863, 4838, 5006, 5359, 6291, 6871, 7077, 7909, 8127, 9245, 9928, 10654, 10889, 12164, 12957, 13764, 14881, 16034, 16343, 16944
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OFFSET
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1,1
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COMMENTS
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A090698 indexed by A000040.
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..1525
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FORMULA
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a(n)=k such that A000040(k) = A090698(n) = 2*A089001(n)^2 + 1.
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EXAMPLE
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From Jon E. Schoenfield, Jan 24 2018: (Start)
prime(8) = 19 = 2*3^2 + 1, so 8 is in the sequence.
prime(21) = 73 = 2*6^2 + 1, so 21 is in the sequence.
prime(33) = 137 = 2*68 + 1, and 68 is not a square, so 33 is not in the sequence. (End)
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MAPLE
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N:= 1000; # to get all entries corresponding to primes <= 2*N^2+1.
R:= select(isprime, [seq(2*k^2+1, k=1..N)]):
A090612:= map(numtheory[pi], R); # Robert Israel, May 09 2014
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MATHEMATICA
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Select[Range[18000], IntegerQ[Sqrt[(Prime[#]-1)/2]]&] (* Harvey P. Dale, Apr 25 2016 *)
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CROSSREFS
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Cf. A089001, A089008, A090698.
Sequence in context: A001471 A162585 A000159 * A212981 A051744 A062443
Adjacent sequences: A090609 A090610 A090611 * A090613 A090614 A090615
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KEYWORD
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nonn
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AUTHOR
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Ray Chandler, Dec 21 2003
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STATUS
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approved
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