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A385303 Decimal expansion of the real number whose continued fraction is Golomb's sequence (A001462).

%I A385303 #18 Jul 02 2025 17:45:33
%S A385303 1,4,1,0,7,8,4,5,3,0,7,4,9,5,3,5,5,9,1,9,3,4,7,9,9,4,2,0,2,1,0,5,7,5,
%T A385303 1,7,8,6,1,4,6,8,6,5,1,7,3,6,6,1,0,8,6,5,1,7,2,5,2,2,6,5,6,4,7,9,6,3,
%U A385303 4,2,1,3,2,2,0,5,1,2,6,7,2,3,6,5,3,2,9,6,3,3,5,6,8,9,8,7,3,8,1,7
%N A385303 Decimal expansion of the real number whose continued fraction is Golomb's sequence (A001462).
%H A385303 Jason Bard, <a href="/A385303/b385303.txt">Table of n, a(n) for n = 1..10000</a>
%e A385303 1.4107845307495355919347994202105751786146865173661...
%t A385303 a[1] = 1; a[n_] := a[n] = 1 + a[n - a[a[n - 1]]]; (* A001462 *)
%t A385303 GenA385303[n_Integer] := Module[{cf1, cf2, d1, d2, i = n}, While[i < 2 n,
%t A385303    cf1 = Table[a[k], {k, 1, i}]; cf2 = Table[a[k], {k, 1, i + 1}];
%t A385303    d1 = RealDigits[FromContinuedFraction[cf1], 10, n+1][[1]]; d2 = RealDigits[FromContinuedFraction[cf2], 10, n+1][[1]];
%t A385303    If[Take[d1,n] === Take[d2,n], Return[Take[d1,n]]]; i++;]];
%t A385303 GenA385303[100]
%Y A385303 Cf. A001462, A060997, A052119.
%K A385303 nonn,cons
%O A385303 1,2
%A A385303 _Jason Bard_, Jun 24 2025