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A056927
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Difference between n^2 and largest prime less than n^2.
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9
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1, 2, 3, 2, 5, 2, 3, 2, 3, 8, 5, 2, 3, 2, 5, 6, 7, 2, 3, 2, 5, 6, 5, 6, 3, 2, 11, 2, 13, 8, 3, 2, 3, 2, 5, 2, 5, 10, 3, 12, 5, 2, 3, 8, 3, 2, 7, 2, 23, 8, 5, 6, 7, 2, 15, 20, 3, 12, 7, 2, 11, 2, 3, 6, 7, 6, 3, 2, 11, 2, 5, 6, 5, 2, 27, 2, 5, 12, 3, 8, 5, 6, 13, 6, 3, 8, 3, 2, 7, 8, 3, 2, 5, 12, 7, 6, 3
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OFFSET
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2,2
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COMMENTS
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Legendre's conjecture (still open) that there is always a prime between n^2 and (n+1)^2 is equivalent to the conjecture that a(n) < 2n-1 for all n>1.
Will the most common subsequence seen be (2,3,2)? - Bill McEachen, Jan 30 2011
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LINKS
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FORMULA
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EXAMPLE
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a(4)=3 because largest prime less than 4^2 is 13 and 16-13=3.
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MAPLE
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MATHEMATICA
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PROG
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(PARI){my(maxx=10000); n=2; ptr=2; while(n<=maxx, q=n^2; pp=precprime(q); diff=q-pp; print(ptr, " ", diff); n++; ptr++ ); } \\ Bill McEachen, May 07 2014
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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