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A302933 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. 21
10, 316, 617610, 803725588973, 456253083482572713037551, 9436780443304881627624731251391047815103579902912, 8811274352857743968291587376477872559585373990088713924172205514999092985039105968614771201466142 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There are only three possible sequences of this kind: one starting from 3 (A302932), another from 4 (A304286) and another from 10 (this sequence).
LINKS
Eric Weisstein's World of Mathematics, Egyptian fraction
Eric Weisstein's World of Mathematics, Trott constants (similar but with continued fractions)
EXAMPLE
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 ...
MAPLE
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);
CROSSREFS
Sequence in context: A119297 A259066 A291561 * A180584 A048345 A325726
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Apr 16 2018
EXTENSIONS
a(4)-a(7) from Giovanni Resta, Apr 16 2018
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)