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A320309
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Numerators of the fractions a(0)/(a(1) - a(0)), a(1)/(a(2) - a(1)), a(2)/(a(3) - a(2)), ... such that the sum 1/a(0) + Sum_{n>=1} a(n-1)/(a(n) - a(n-1)) has the concatenation of these numerators as decimal part. Case a(0) = 38.
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15
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OFFSET
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0,1
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COMMENTS
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It appears that fractions of this kind exist only for a(0) equal to 3 (A320306), 10 (A320307), 13 (A320308) and 38 (this sequence).
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LINKS
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EXAMPLE
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1/38 = 0.02631...
At the beginning instead of 38 we have 02 as first decimal digits. Adding the second term this is fixed.
1/38 + 38/(145 - 38) = 0.38145597...
1/38 + 38/(145 - 38) + 145/(78285806 - 145) = 0.3814559778285806137...
The sum is 0.38 145 78285806 956422831811259761822 ...
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MAPLE
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P:=proc(q, h) local a, b, d, n, t, x; x:=h+1; a:=1/h; b:=ilog10(h)+1;
d:=h; print(d); t:=1/a; for n from x to q do if
trunc(evalf(a+t/(n-t), 100)*10^(b+ilog10(n)+1))=d*10^(ilog10(n)+1)+n
then b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+t/(n-t); t:=n;
x:=n+1; print(n); fi; od; end: P(10^20, 38);
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CROSSREFS
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Cf. A302932, A302933, A303388, A304285, A304286, A304287, A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A320306, A320307, A320308.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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