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Search: id:A155557
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| A155557 |
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A proximate-prime polynomial sequence generated by 2n^2 - 2n + 53089. Produces 634 primes in the first 1000 terms. (A proximate-prime polynomial is a finite polynomial equation that is derived from four successive - proximate, or neighboring - primes.) |
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| 53089, 53093, 53101, 53113, 53129, 53149, 53173, 53201, 53233, 53269, 53309, 53353, 53401, 53453, 53509, 53569, 53633, 53701, 53773, 53849, 53929, 54013, 54101, 54193, 54289, 54389, 54493, 54601, 54713, 54829
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Quadratic derived from four successive primes: 53089, 53093, 53101, 53113. Produces more primes in the first 1000 terms than any other quadratic derived from 4 successive primes under 1000000. (This includes 41, 43, 47, 53 = n^2 - n + 41, which produces 582.)
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LINKS
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The High Primality of Prime-Derived Quadratic Sequences
Wolfram Mathworld: Prime-Generating Polynomial
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FORMULA
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2n^2 - 2n + 53089
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EXAMPLE
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For n=14, 2*(14^2)-(2*14)+53089 = 53453
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PROGRAM
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(Other) QTest: Derive, analyze and solve quadratic expressions. Generate integer sequences and determine their primality. (http://www.naturalnumbers.org/QTest-NTK.html)
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CROSSREFS
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A140947, A126665, A126719, A127316
Sequence in context: A058326 A157758 A031833 this_sequence A015315 A061330 A164519
Adjacent sequences: A155554 A155555 A155556 this_sequence A155558 A155559 A155560
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Michael M. Ross (michaelmross(AT)gmail.com), Jan 24 2009
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