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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 Cf. A302932, A303388, A304286. Sequence in context: A119297 A259066 A291561 * A180584 A048345 A325726 Adjacent sequences:  A302930 A302931 A302932 * A302934 A302935 A302936 KEYWORD nonn,base AUTHOR Paolo P. Lava, Apr 16 2018 EXTENSIONS a(4)-a(7) from Giovanni Resta, 16 Apr 2018 STATUS approved

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Last modified May 29 04:17 EDT 2020. Contains 334696 sequences. (Running on oeis4.)