%I #36 Mar 03 2024 08:35:44
%S 10,316,617610,803725588973,456253083482572713037551,
%T 9436780443304881627624731251391047815103579902912,
%U 8811274352857743968291587376477872559585373990088713924172205514999092985039105968614771201466142
%N 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.
%C There are only three possible sequences of this kind: one starting from 3 (A302932), another from 4 (A304286) and another from 10 (this sequence).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EgyptianFraction.html">Egyptian fraction</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TrottConstants.html">Trott constants (similar but with continued fractions)</a>
%e We start from 10 because 1/10 = 0.1000...
%e Then the next integer is 316 because 1/10 + 1/316 = 0.10316455... and so on.
%e The sum is 0.10 316 617610 803725588973 456253083482572713037551 ...
%p P:=proc(q) local a,b,d,n; a:=1/10; b:=2; d:=10; print(d);
%p 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;
%p od; end: P(10^20);
%Y Cf. A302932, A303388, A304286.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Apr 16 2018
%E a(4)-a(7) from _Giovanni Resta_, Apr 16 2018