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A091015
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Least integer x>0 such that x^2=ceiling(x*r*floor(x/r)) where r=sqrt(n).
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0
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1, 3, 2, 2, 9, 5, 8, 3, 3, 19, 10, 7, 649, 15, 4, 4, 33, 17, 170, 9, 55, 197, 24, 5, 5, 51, 26, 127, 9801, 11, 1520, 17, 23, 35, 6, 6, 73, 37, 25, 19, 2049, 13, 3482, 199, 161, 24335, 48, 7, 7, 99, 50, 649, 66249, 485, 89, 15, 151, 19603, 530, 31
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OFFSET
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1,2
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COMMENTS
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For r=sqrt(n), the solutions to x^2=ceiling(x*r*floor(x/r)) appear to be given by the Chebyshev polynomial T(k,x) k>0 evaluated at x=a(n). These solutions also seem to be given by a sequence (b(k))_(k>=0) satisfying the recurrence b(k)= 2*A002350(n)*b(k-1)-b(k-2).
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LINKS
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PROG
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(PARI) a(n)=if(n<2, 1, x=1; while(abs(x^2-ceil(sqrt(n)*x*floor(x/ sqrt(n))))>0, x++); x)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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