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Search: id:A109619
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| A109619 |
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Smallest prime p such that 2n+p is the square of a prime, or 0 if no such prime exists. At present the 0 terms are conjectural and open to correction, indicating only that the term is 0 or greater than the 1000000th prime. |
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+0
1
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| 2, 5, 3, 17, 0, 13, 11, 0, 7, 5, 3, 97, 23, 0, 19, 17, 0, 13, 11, 0
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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It appears that for many values of m in the arithmetic progression 4,10,16,22,...,4+6k,..., there may not exist a prime p such that m+p is the square of a prime. For most other values of m<40 there are 70-170 primes less than Prime(1000000) such that m+p is the square of a prime.
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EXAMPLE
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For n=4, we find that 17+2*4=25=5^2 and no smaller prime than 17 works, so a(4)=17. For n=5, calculation shows that 10+p is not the square of a prime where p is any of the first one million primes; thus a(5)=0.
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CROSSREFS
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Sequence in context: A035334 A002565 A063703 this_sequence A087228 A077216 A058357
Adjacent sequences: A109616 A109617 A109618 this_sequence A109620 A109621 A109622
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Aug 01 2005
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