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Smallest missing number in first 10^n digits after the decimal point in the expansion of Pi.
4

%I #41 Aug 10 2019 02:36:46

%S 0,12,103,1001,10000,14523,106945,1001823,10007363,100023783,

%T 1000020346

%N Smallest missing number in first 10^n digits after the decimal point in the expansion of Pi.

%H Peter TrĂ¼b, <a href="https://pi2e.ch/blog/2017/03/10/pi-digits-download/">22.4 trillion digits of pi</a>

%e a(1) = 0 because 0 is missing in the first 10^1 = 10 digits after the decimal point in the expansion of Pi, that is, .1415926535...

%e Leading zeros do not count. Thus each of the digit-strings "0", "1", "2", ..., "14522" is present in the first 10^6 digits after the decimal point, but "14523" is not, so a(6) = 14523. - _Robert Israel_, Oct 19 2015

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

%o (Python)

%o start = 0

%o for a in range(1,10):

%o ....with open("pi-billion.txt","r") as f:

%o ........g = f.read(10**a)

%o ....while g.find(str(start)) != -1:

%o ........start += 1

%o ....print(a,start)

%o # http://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt

%o # _David Consiglio, Jr._, Oct 25 2014

%Y Cf. A000796, A228989, A228990, A260627, A260628.

%K nonn,base,more

%O 1,2

%A _Shyam Sunder Gupta_, Sep 10 2013

%E More terms from _David Consiglio, Jr._, Oct 25 2015

%E a(10)-a(11) from _Giovanni Resta_, Aug 10 2019