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A302932 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) = 3. 22
3, 52, 58130, 684605953, 18209086488275508678, 62003660502140726224833872663126972818, 8808009238542973573505163998155451603728137116913210531450093169728092387825 (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 (this sequence), another from 4 (A304286) and another from 10 (A302933).

Next term a(8) has 152 digits (see b-file). - Giovanni Resta, Apr 16 2018

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..8

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 3 because 1/3 = 0.3333...

Then the next integer is 52 because 1/3 + 1/52 = 0.352564... and so on.

The sum is 0.3 52 58130 684605953 18209086488275508678 ...

MAPLE

P:=proc(q) local a, b, d, n; a:=1/3; b:=1; d:=3; 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

Cf. A302933, A303388, A304286.

Sequence in context: A263530 A136723 A202649 * A143387 A228452 A269458

Adjacent sequences:  A302929 A302930 A302931 * A302933 A302934 A302935

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 June 5 15:37 EDT 2020. Contains 334852 sequences. (Running on oeis4.)