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A302933
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Sequence gives the denominators, in increasing values, of Egyptian fractions such that their sum has the concatenation of these denominators as decimal part. Case a(1) = 10.
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21
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10, 316, 617610, 803725588973, 456253083482572713037551, 9436780443304881627624731251391047815103579902912, 8811274352857743968291587376477872559585373990088713924172205514999092985039105968614771201466142
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OFFSET
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1,1
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COMMENTS
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There are only three possible sequences of this kind: one starting from 3 (A302932), another from 4 (A304286) and another from 10 (this sequence).
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LINKS
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EXAMPLE
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We start from 10 because 1/10 = 0.1000...
Then the next integer is 316 because 1/10 + 1/316 = 0.10316455... and so on.
The sum is 0.10 316 617610 803725588973 456253083482572713037551 ...
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MAPLE
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P:=proc(q) local a, b, d, n; a:=1/10; b:=2; d:=10; print(d);
for n from 1 to q do if trunc(evalf(a+1/n, 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+1/n; print(n); fi;
od; end: P(10^20);
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CROSSREFS
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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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