This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A280546 #19 May 29 2024 06:58:35
%S A280546 2,19,150,953,2708,32414,158810,4602784,472173970,472173970
%N A280546 Index in A002193 of start of first occurrence of at least n consecutive equal digits in the decimal expansion of sqrt(2) after the decimal point.
%C A280546 We index the digits of sqrt(2) = 1.4142135... starting with 1 (for the 1), 2 (for the 4), 3 (for the second 1), 4 (for the second 4), 5 (for the 2), and so on.
%C A280546 Find the index of the first digit of a run of n consecutive equal digits after the decimal point: this is a(n). For example, the "88" here 1414213562373095048801.. begins at the 19th digit, so a(2) = 19. - _N. J. A. Sloane_, Mar 20 2023
%H A280546 <a href="http://www.subidiom.com/pi/">Irrational Numbers Search Engine</a> (searches initial 2 x 10^9 digits of sqrt(2))
%t A280546 Module[{nn=160000,s2},s2=RealDigits[Sqrt[2],10,nn][[1]];Flatten[Table[ SequencePosition[ s2,PadRight[{},k,x_],1],{k,7}],1]][[;;,1]] (* _Harvey P. Dale_, Mar 20 2023 *)
%o A280546 (PARI) string(n) = default(realprecision, n+10); my(x=sqrt(2)); floor(x*10^n)
%o A280546 digit(n) = string(n)-10*string(n-1)
%o A280546 searchstrpos(n) = my(x=1, i=1); while(1, my(y=x+1); while(digit(y)==digit(x), y++; i++); if(i >= n, return(x+1)); i=1; x++)
%o A280546 a(n) = searchstrpos(n)
%Y A280546 Cf. A002193, A244601, A277259, A277532.
%K A280546 nonn,base,more
%O A280546 1,1
%A A280546 _Felix Fröhlich_, Jan 05 2017