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Smallest missing number in first 10^n digits after the decimal point in expansion of golden ratio phi = (1+sqrt(5))/2.
2

%I #21 Mar 27 2020 02:54:21

%S 2,10,100,1001,10002,49107,119904,1015528

%N Smallest missing number in first 10^n digits after the decimal point in expansion of golden ratio phi = (1+sqrt(5))/2.

%e a(1) = 2 because number 2 is missing in first 10^1 = 10 digits after decimal point in the decimal expansion of the golden ratio, that is, 1.6180339887.

%t Do[With[{r = ToString[FromDigits[Rest[RealDigits[GoldenRatio, 10, 10^k][[1]]]]]}, Do[If[StringPosition[r, ToString[n]] == {}, Print[n]; k = k + 1; Break[]], {n, 0, 10000000}]], {k, 1, 7}]

%Y Cf. A001622, A228988, A228989.

%K nonn,base,more

%O 1,1

%A _Shyam Sunder Gupta_, Sep 10 2013

%E Name improved by _Alex Ratushnyak_, Sep 22 2013

%E a(8) from _Jinyuan Wang_, Mar 27 2020