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.

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

Offset: 1

Author

Felix Fröhlich, Jan 05 2017

Keywords

• nonn
• base
• more

Comments

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.

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

Links

• Irrational Numbers Search Engine (searches initial 2 x 10^9 digits of sqrt(2))

Crossrefs

Cf. A002193, A244601, A277259, A277532.

Programs

Mathematica

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 *)

PARI

string(n) = default(realprecision, n+10); my(x=sqrt(2)); floor(x*10^n)
digit(n) = string(n)-10*string(n-1)
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++)
a(n) = searchstrpos(n)