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A307007
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a(n) is defined by the condition that the decimal expansion of the Sum_{n>=1} 1/(n*a(n)) = 1/(1*a(1)) + 1/(2*a(2)) + 1/(3*a(3)) + ... begins with the concatenation of these numbers; also a(1) = 3 and a(n) > a(n-1).
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7
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3, 44, 70171, 99999262192, 91098508760349172092, 970792725489545464249914539975116316038, 931700887896779243871964259462997210573060273337039138324846507043947496698605
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OFFSET
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1,1
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COMMENTS
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If we had Sum_{n>=1} (-1)^(n-1)/(n*a(n)) = 1/(1*a(1)) - 1/(2*a(2)) + 1/(3*a(3)) - ... the terms would be only 3, 317, 61469 because we get 0.3317614690547... and the zero after 61469 cannot be covered by any number.
At any step only the least value greater than a(n) is taken into consideration. As a(2) we could choose 44, 347, 3348, 33348, ..., 3...348. Again, if a(2) = 44 then we could choose as a(3) 70171, 697447, ...
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LINKS
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EXAMPLE
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1/(1*3) = 0.3333...
1/(1*3) + 1/(2*44) = 0.344696...
1/(1*3) + 1/(2*44) + 1/(3*70171) = 0.34470171999...
The sum is 0.3 44 70171 99999262192 ...
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MAPLE
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P:=proc(q, h) local a, b, d, n, t, z; a:=1/h; b:=ilog10(h)+1;
d:=h; print(d); t:=2; for n from 1 to q do
z:=evalf(evalf(a+1/(t*n), 100)*10^(b+ilog10(n)+1), 100);
z:=trunc(z-frac(z)); if z=d*10^(ilog10(n)+1)+n
then b:=b+ilog10(n)+1; d:=d*10^(ilog10(n)+1)+n; a:=a+1/(t*n); t:=t+1;
print(n); fi; od; end: P(10^9, 3);
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CROSSREFS
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Cf. A304288, A304289, A305661, A305662, A305663, A305664, A305665, A305666, A305667, A305668, A320023, A320284, A320306, A320307, A320308, A320309, A320335, A320336, A324222, A324223.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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