A280546 - OEIS

%I #19 May 29 2024 06:58:35

%S 2,19,150,953,2708,32414,158810,4602784,472173970,472173970

%N 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 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 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 <a href="http://www.subidiom.com/pi/">Irrational Numbers Search Engine</a> (searches initial 2 x 10^9 digits of sqrt(2))

%t 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 (PARI) string(n) = default(realprecision, n+10); my(x=sqrt(2)); floor(x*10^n)

%o digit(n) = string(n)-10*string(n-1)

%o 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 a(n) = searchstrpos(n)

%Y Cf. A002193, A244601, A277259, A277532.

%K nonn,base,more

%O 1,1

%A _Felix Fröhlich_, Jan 05 2017