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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: A136723 A202649 A347611 * 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 August 12 11:14 EDT 2022. Contains 356069 sequences. (Running on oeis4.)